Physics Grade 12 new textbook.pdf

# Application of physics in other fields This unit explores the extensive applications of physics across various scientific disciplines and technological advancements, highlighting its fundamental role in chemistry, biology, astronomy, geology, engineering, medicine, and defense. ### 1.1 Physics and other sciences Physics is a foundational science that significantly influences and underpins many other scientific disciplines. The understanding of fundamental physical laws is crucial for advancements in various fields [5](#page=5). #### 1.1.1 Relation of Physics with chemistry Physics and chemistry share common ground when examining matter composed of electrons and nuclei. Fundamental laws governing matter's behavior are applicable to both fields, as both are concerned with matter and its interaction with energy. Concepts in atomic and subatomic particle physics are essential for understanding covalent bonding, molecule formation, and the energetic favorability of chemical bonds. Physics principles related to heat energy help chemists predict reaction feasibility and equilibrium compositions, bridging macroscopic properties with molecular behavior. Spectroscopy, a key tool in both physics and chemistry, studies the interaction between matter and electromagnetic radiation and is vital for understanding atomic and molecular structures. Ultimately, the study of matter and electricity in physics is fundamental to understanding chemical concepts such as atomic structure, molecular structure, X-ray diffraction, radioactivity, and chemical bonding [5](#page=5) [6](#page=6). #### 1.1.2 Relation of Physics and biology Physics provides essential principles for understanding biological processes, from the mechanics of human motion to the fluid dynamics of blood flow [7](#page=7). * **Newtonian mechanics** explains the motion and equilibrium of living systems. It helps understand how animals move, why certain animals are faster than others, and the principles of stability based on the center of mass and base of support (#page=6, 7) [6](#page=6) [7](#page=7). * **Fluid flow physics** (viscosity, continuity equation, turbulent flow) is critical for understanding blood circulation and blood pressure in multicellular organisms [7](#page=7). * **Sound wave physics** explains sound production in humans. Vibrating vocal folds generate sound waves during exhalation, which propagate to the ear and are interpreted by the brain (#page=7, 8) [7](#page=7) [8](#page=8). * **Electrical physics** is fundamental to understanding life processes involving electrical phenomena, such as nerve signal transmission and muscle control. Neurons transmit information as electrical pulses. Sharks, for example, use specialized electro-sensitive organs to detect weak electric fields [8](#page=8). * **Optical physics** is crucial as light, particularly from the sun, is vital for life. Photosynthesis in plants utilizes light energy, and animal eyes use light as their primary source of information about their surroundings. Optics also encompasses microscopes, telescopes, and lasers, all with significant applications in life sciences [8](#page=8). > **Tip:** Understanding how athletes move or why an earthworm locomotes without limbs are excellent examples of Newtonian mechanics and fluid dynamics applied to biology, respectively. ### 1.2 Relation of Physics and Astronomy Astrophysics, the study of celestial objects, heavily relies on physics principles to understand the universe [9](#page=9). * **Newton's laws of motion and gravitation** are used to describe the motion of celestial bodies like planets around the sun and moons around planets. Concepts of centripetal and centrifugal forces explain orbital mechanics [9](#page=9). * **Electromagnetic wave physics** is crucial for astronomers to gather information about distant objects. Telescopes detect various parts of the electromagnetic spectrum (radio, infrared, optical) (#page=9, 10. The apparent brightness of an object is related to its distance by the inverse square law: $apparent\ brightness \propto \frac{true\ brightness}{distance^2}$. Astronomers also use the light-year as a unit of distance [10](#page=10) [9](#page=9). * **Atomic physics** is vital for understanding the composition, temperature, and motion of astronomical objects. Light emitted or absorbed by celestial bodies arises from atomic transitions, where electrons move between energy orbits, emitting or absorbing photons (#page=10, 11). Studying these spectral lines provides detailed information about stellar composition and temperature [10](#page=10) [11](#page=11). > **Example:** Astronomers use the red-shift of light from distant galaxies, a phenomenon explained by the Doppler effect on electromagnetic waves, to determine their recession velocity and thus infer the expansion of the universe. ### 1.3 Relation of Physics with Geology Geology, a branch of Earth science, studies the solid and liquid matter of the Earth and the processes affecting it. Understanding geological processes requires knowledge of various physics concepts [11](#page=11): * **Force, optics, atomic structure, electromagnetic radiation, heat and heat flow, electricity and magnetism, stress and strain, waves (including sound waves), and fluid flow** are all applied in geology [12](#page=12). * These physics concepts are used to study the electrical properties, density, magnetization, radioactivity, and elasticity of rocks and minerals. Geologists use wave propagation to study subterranean structures without excavation [12](#page=12). ### 1.4 Physics and Engineering Physics provides the fundamental knowledge upon which various branches of engineering are built. Engineering disciplines like civil, mechanical, and electrical engineering are governed by physical laws, making an understanding of physics essential for solving complex engineering problems (#page=12, 13 [12](#page=12) [13](#page=13). * **Civil Engineering** uses physics principles like forces, fluid pressure, and gravity for designing and constructing structures such as skyscrapers, roads, bridges, and dams [13](#page=13). * **Mechanical Engineering** applies concepts from mechanics, dynamics, thermodynamics, forces, and stresses to create mechanical systems like engines, vehicles, and robotics [13](#page=13). * **Electrical Engineering** involves designing electrical circuits, motors, and communication systems, requiring knowledge of electromagnetism, mechanics, and thermodynamics to convert electrical energy into other forms [14](#page=14). * **Chemical Engineering** relies on the laws of physical chemistry and physics, including molecular physics and thermodynamics, to design processes for refining raw materials and producing chemicals (#page=14, 15 [14](#page=14) [15](#page=15). #### Technology generating new physics There is a reciprocal relationship between physics and technology. While physics enables technological advancements, technology also drives the development of new physics discoveries. Modern scientific experiments often depend on advanced technology, and technologies like X-ray discovery have significantly contributed to physics research, including the study of atomic structure [15](#page=15). > **Tip:** The development of the synchrotron, a technology born from particle accelerators, has revolutionized many areas of physics and chemistry by providing intense beams of X-rays for various experimental studies. ### 1.5 Medical physics Medical physics applies physics principles to diagnose and treat medical conditions. The discovery of X-rays by Wilhelm Conrad Roentgen in 1895 marked the beginning of this interdisciplinary field [16](#page=16). * **Medical Imaging** uses various technologies to view the human body. Techniques include electromagnetic methods (optical, X-ray, MRI, thermography), acoustic methods (ultrasound), and chemical and electrical methods [16](#page=16). * **Magnetic Resonance Imaging (MRI)**: MRI utilizes the principle of magnetic resonance, where atomic nuclei (specifically protons in water molecules) absorb and emit electromagnetic radiation in the presence of magnetic fields (#page=16, 17). Protons in a magnetic field align and, when pulsed with radio waves, flip. As they return to their aligned state, they release energy, which is detected and processed into detailed images of soft tissues [16](#page=16) [17](#page=17). * **X-Ray Computerized Tomography (CT Scan)**: X-ray imaging works by measuring the differential absorption of X-rays as they pass through tissues of varying densities. CT scans use rotating X-ray machines and detectors to create cross-sectional images (tomograms) of the body, providing more detail than conventional X-rays [17](#page=17) [18](#page=18). * **Ultrasound**: Ultrasound uses sound waves with frequencies above 20 KHz (typically 3.5-10 MHz). These waves penetrate tissues and are reflected, scattered, and absorbed. The reflected waves are detected and used to create images. Tissues reflect ultrasound differently, resulting in images with varying echogenicity: anechoic (black, fluid-filled), hypoechoic (dark gray, fewer echoes), and hyperechoic (light gray, many echoes) (#page=18, 19) [18](#page=18) [19](#page=19). * **Stethoscopes** are a familiar clinical use of sound to analyze body sounds like heartbeats and lung sounds [18](#page=18). * **Radiation Therapy**: High-energy photons (X-rays, gamma rays) and particles from radioactive nuclei can damage biological molecules and are used therapeutically to treat cancer (#page=19, 20). Radioactive materials can be implanted near tumors, or external beams of radiation can be directed at cancerous growths, with careful control to minimize damage to healthy tissues [19](#page=19) [20](#page=20). > **Example:** MRI can distinguish between different types of brain tissue (gray matter, white matter, blood) because the protons in each tissue type release slightly different amounts of energy after being excited by radio waves. ### 1.6 Physics and Defense Technology Modern defense forces extensively utilize advancements in physics, including optics, electromagnetism, atomic and nuclear physics, and materials science [20](#page=20). * **Radar Technology**: RADAR (Radio Detection And Ranging) uses electromagnetic signals to detect and track objects. It calculates the range (R) of a target by measuring the time (t) it takes for a signal to travel to the target and back, using the formula $R = \frac{ct}{2}$, where c is the speed of light. Radar is crucial for military applications like air defense, target detection, and weapon guidance, as well as civilian uses like air traffic control and weather observation [21](#page=21). * **Missiles**: Missiles are propelled weapons that deliver explosive payloads with accuracy. Their flight can be governed by Newtonian mechanics (ballistic missiles) or controlled by thrust adjustments (cruise missiles). They comprise complex electronic, digital, and mechanical subsystems for guidance, stabilization, propulsion, and target tracking [22](#page=22). * **Infrared (IR) Wave Detection for Night Vision**: Human eyes are sensitive to visible light, but infrared radiation, just outside this range, can be detected by specialized devices. All objects emit infrared light proportional to their temperature. Infrared vision systems, such as night vision goggles, use thermal emissions to identify objects that are not visible in low light conditions. They create images based on temperature differences, often displaying them in green for optimal human visual perception [23](#page=23). > **Tip:** The principle behind radar is similar to how we perceive distance with our eyes: we estimate how long it takes for something to "return" our "signal" (light reflecting off it). ### 1.7 Physics in Communication Communication technologies, essential in modern life, rely heavily on physics principles, particularly electromagnetic theory [24](#page=24). * **Communication Systems**: Communication involves transferring information, classified as wired or wireless. Wireless systems use radio waves, microwaves, and infrared waves, while wired systems use wires and optical fibers [24](#page=24). * **Physics Concepts**: Understanding electromagnetic theory is crucial for radio waves, microwaves, and infrared waves used in wireless and fiber optic communication. Concepts like electricity and magnetism, electrical circuits, wave phenomena (reflection, diffraction, refraction, interference), and energy transformations are also vital [24](#page=24). --- # Two-dimensional motion Two-dimensional motion describes the movement of objects along a plane, encompassing scenarios beyond simple straight-line paths, and it is governed by fundamental principles of kinematics and dynamics [28](#page=28). ### 2.1 Projectile motion Projectile motion refers to the movement of an object that is in flight after being thrown or projected, and it is subject only to the acceleration due to gravity. Key examples include a kicked football, a fired bullet, or a thrown javelin. For analysis, two assumptions are made: the free-fall acceleration due to gravity ($g$) is constant and directed downwards, and air resistance is negligible. Under these assumptions, the path of a projectile, known as its trajectory, is a parabola. The horizontal and vertical components of a projectile's motion are independent and can be analyzed separately using time as the common variable [29](#page=29) [30](#page=30). #### 2.1.1 Horizontal projection In horizontal projection, an object is launched horizontally from a certain height. Its initial vertical velocity is zero, and it possesses only an initial horizontal velocity [30](#page=30). * **Horizontal motion:** The horizontal acceleration is zero, so the initial horizontal velocity ($v_{0x}$) remains constant throughout the flight. The final horizontal velocity ($v_x$) is given by [30](#page=30): $v_x = v_{0x}$ [30](#page=30). The horizontal distance ($\Delta x$) traveled at time $t$ is: $\Delta x = v_{0x} t$ [30](#page=30). * **Vertical motion:** This is a constant accelerated motion with acceleration $g = -9.8 \, \text{m/s}^2$. The kinematic equations for constant accelerated motion apply [31](#page=31): $v_y = v_{0y} + gt$ [31](#page=31). Since $v_{0y} = 0$ for horizontal projection: $v_y = gt$ [31](#page=31). The vertical displacement ($\Delta y$) is: $\Delta y = v_{0y} t + \frac{1}{2} gt^2$ [31](#page=31). With $v_{0y} = 0$: $\Delta y = \frac{1}{2} gt^2$ [31](#page=31). * **Time of Flight:** The time taken for the projectile to hit the ground. From the vertical displacement equation: $t = \sqrt{\frac{2\Delta y}{g}}$ [32](#page=32). Note that $\Delta y$ and $g$ are considered negative for downward motion [32](#page=32). * **Range (R):** The maximum horizontal distance traveled by the projectile. It is calculated using the time of flight: $R = v_{0x} t$ [32](#page=32). Substituting the time of flight: $R = v_{0x} \sqrt{\frac{2\Delta y}{g}}$ [32](#page=32). > **Example 2.1:** A rifle is aimed horizontally at a target 30m away. The bullet hits 2 cm below the aiming point. > (a) Time of flight: $\Delta y = \frac{1}{2} gt^2 \implies -0.02 \, \text{m} = \frac{1}{2} (-10 \, \text{m/s}^2) t^2 \implies t \approx 0.06 \, \text{s}$ [32](#page=32). > (b) Initial velocity: $v_{0x} = \frac{\Delta x}{t} = \frac{30 \, \text{m}}{0.06 \, \text{s}} = 500 \, \text{m/s}$ [33](#page=33). > **Example 2.2:** An airplane flying at 100 m/s horizontally drops a food package from 300m. > (a) Time to reach the ground: $\Delta y = \frac{1}{2} gt^2 \implies -300 \, \text{m} = \frac{1}{2} (-10 \, \text{m/s}^2) t^2 \implies t \approx 7.74 \, \text{s}$ [33](#page=33). > (b) Distance from the car driver: $\Delta x = v_{0x} t = 100 \, \text{m/s} \times 7.74 \, \text{s} = 774 \, \text{m}$ [33](#page=33). #### 2.1.2 Inclined projectile motion In inclined projectile motion, an object is projected with an initial velocity $v_0$ at an angle $\theta$ with the horizontal. The initial velocity can be resolved into horizontal ($v_{0x}$) and vertical ($v_{0y}$) components [35](#page=35): $v_{0x} = v_0 \cos\theta$ [36](#page=36). $v_{0y} = v_0 \sin\theta$ [36](#page=36). * **Horizontal motion:** The velocity remains constant ($v_x = v_0 \cos\theta$) because there is no horizontal acceleration. The horizontal displacement at time $t$ is [35](#page=35): $\Delta x = v_0 \cos\theta \, t$ [36](#page=36). * **Vertical motion:** The vertical velocity changes with time due to gravity ($g = -9.8 \, \text{m/s}^2$). The vertical velocity at time $t$ is [35](#page=35): $v_y = v_0 \sin\theta + gt$ [36](#page=36). The vertical displacement at time $t$ is: $\Delta y = v_0 \sin\theta \, t + \frac{1}{2} gt^2$ [36](#page=36). * **Time to reach maximum height:** At the maximum height, the vertical component of velocity ($v_y$) is zero [35](#page=35). $0 = v_0 \sin\theta + gt \implies t_{\text{max height}} = \frac{v_0 \sin\theta}{g}$ [36](#page=36). * **Time of Flight:** The total time the projectile is in the air. If the launch and landing points are at the same horizontal level ($\Delta y = 0$): $0 = v_0 \sin\theta \, t + \frac{1}{2} gt^2$ [37](#page=37). $t_{\text{total}} = \frac{2v_0 \sin\theta}{g}$ [37](#page=37). This formula is not valid if the landing elevation differs from the launch elevation [37](#page=37). * **Horizontal Range (R):** The maximum horizontal distance traveled when the launch and landing points are at the same horizontal level. $R = v_0 \cos\theta \, t_{\text{total}} = \frac{v_0^2 \sin(2\theta)}{g}$ [38](#page=38). The range is maximum when $\theta = 45^\circ$. The same range is achieved for launch angles that sum to $90^\circ$ [38](#page=38). * **Maximum Height (H):** The maximum vertical displacement. $H = \frac{v_0^2 \sin^2\theta}{2g}$ [39](#page=39). * **Relation between Range and Maximum Height:** For a projectile launched and landing at the same level: $\frac{H}{R} = \frac{\sin\theta}{4\cos\theta} \implies H = \frac{R \tan\theta}{4}$ [39](#page=39). > **Example 2.3:** A football is kicked at $37^\circ$ with an initial velocity of 40 m/s. > (a) Maximum height: $H = \frac{(40 \, \text{m/s})^2 \sin^2(37^\circ)}{2 \times 10 \, \text{m/s}^2} \approx 28.8 \, \text{m}$ [39](#page=39). > (b) Horizontal range: $R = \frac{(40 \, \text{m/s})^2 \sin(2 \times 37^\circ)}{10 \, \text{m/s}^2} \approx 153.8 \, \text{m}$ [40](#page=40). > **Example 2.4:** A ball is thrown with a speed of 25 m/s at an angle of $53^\circ$ towards a wall 24m away. > (a) Time to reach the wall: $t = \frac{\Delta x}{v_0 \cos\theta} = \frac{24 \, \text{m}}{25 \, \text{m/s} \times \cos(53^\circ)} \approx 1.6 \, \text{s}$ [41](#page=41). > (b) Height above release point: $\Delta y = v_0 \sin\theta \, t + \frac{1}{2} gt^2 = (25 \, \text{m/s}) \sin(53^\circ) (1.6 \, \text{s}) + \frac{1}{2} (-10 \, \text{m/s}^2) (1.6 \, \text{s})^2 \approx 19.2 \, \text{m}$ [41](#page=41). > (c) Velocity components at impact: $v_x = v_0 \cos\theta = 25 \, \text{m/s} \times 0.6 = 15 \, \text{m/s}$; $v_y = v_0 \sin\theta + gt = (25 \, \text{m/s}) \sin(53^\circ) + (-10 \, \text{m/s}^2) (1.6 \, \text{s}) \approx 10 \, \text{m/s}$ [41](#page=41). ### 2.2 Rotational motion Rotational motion describes the movement of a rigid body where all its particles move in circular paths around a fixed axis with a common angular velocity. A rigid body has a perfectly defined and unchanging shape [42](#page=42) [43](#page=43). * **Angular Displacement ($\Delta\theta$):** The change in angular position, measured in radians or degrees. The relationship between arc length ($s$), radius ($r$), and angular displacement ($\theta$) is [43](#page=43): $s = r \theta$ [43](#page=43). Angular displacement is defined as: $\Delta\theta = \theta_f - \theta_0$ [43](#page=43). * **Angular Velocity ($\omega$):** The rate of change of angular displacement. The average angular velocity ($\omega_{\text{av}}$) is: $\omega_{\text{av}} = \frac{\Delta\theta}{\Delta t}$ [44](#page=44). Units are radians per second (rad/s) [44](#page=44). * **Angular Acceleration ($\alpha$):** The rate of change of angular velocity. The average angular acceleration ($\alpha_{\text{av}}$) is: $\alpha_{\text{av}} = \frac{\Delta\omega}{\Delta t}$ [44](#page=44). Units are radians per second squared (rad/s$^2$) [44](#page=44). Angular velocity and acceleration are vector quantities, with directions along the axis of rotation, determined by the right-hand rule [44](#page=44). #### 2.2.1 Equations of motion for uniform angular acceleration For constant angular acceleration, the kinematic equations for rotational motion are analogous to those for linear motion: * $\omega_f = \omega_o + \alpha \Delta t$ [45](#page=45). * $\Delta\theta = \omega_o \Delta t + \frac{1}{2} \alpha \Delta t^2$ [45](#page=45). * $\omega_f^2 = \omega_o^2 + 2\alpha \Delta\theta$ [45](#page=45). > **Example 2.5:** A wheel's angular speed changes from 30 rad/s to 50 rad/s in 2 seconds. > Average angular acceleration: $\alpha_{\text{av}} = \frac{50 \, \text{rad/s} - 30 \, \text{rad/s}}{2 \, \text{s}} = 10 \, \text{rad/s}^2$ [46](#page=46). > **Example 2.6:** A wheel with initial angular velocity 10 rad/s accelerates at 2.5 rad/s$^2$. > (a) Revolutions in 30 s: $\Delta\theta = (10 \, \text{rad/s})(30 \, \text{s}) + \frac{1}{2} (2.5 \, \text{rad/s}^2)(30 \, \text{s})^2 = 1425 \, \text{rad} \approx 226.9 \, \text{rev}$ [47](#page=47). > (b) Angular speed at t = 20 s: $\omega_f = 10 \, \text{rad/s} + (2.5 \, \text{rad/s}^2)(20 \, \text{s}) = 60 \, \text{rad/s}$ [47](#page=47). #### 2.2.2 Relationship between angular and translational quantities For a point on a rotating rigid object at a distance $r$ from the axis of rotation: * **Tangential speed (v):** $v = \omega r$ [50](#page=50). * **Tangential acceleration ($a_t$):** $a_t = \alpha r$ [50](#page=50). > **Example 2.8:** A wheel of radius 20 cm accelerates from rest to 15 rev/s in 30 s. > Angular acceleration: $\alpha = \frac{15 \, \text{rev/s} - 0}{30 \, \text{s}} = 0.5 \, \text{rev/s}^2 = \pi \, \text{rad/s}^2$ [48](#page=48). > Tangential acceleration: $a_t = \alpha r = (\pi \, \text{rad/s}^2)(0.2 \, \text{m}) \approx 0.6 \, \text{m/s}^2$ [48](#page=48). > **Example 2.9:** A car accelerates from 20 m/s to 24 m/s in 5 s. The wheels have a radius of 40 cm. > Tangential acceleration: $a_t = \frac{24 \, \text{m/s} - 20 \, \text{m/s}}{5 \, \text{s}} = 0.8 \, \text{m/s}^2$ [49](#page=49). > Angular acceleration: $\alpha = \frac{a_t}{r} = \frac{0.8 \, \text{m/s}^2}{0.4 \, \text{m}} = 2 \, \text{rad/s}^2$ [49](#page=49). ### 2.3 Rotational dynamics Rotational dynamics deals with the causes of rotational motion. * **Torque ($\tau$):** The rotational effect of a force. It causes angular acceleration. The magnitude of torque is given by [53](#page=53): $\tau = r F \sin\theta$ [53](#page=53). where $r$ is the distance from the axis of rotation to the point of force application, and $\theta$ is the angle between $r$ and $F$. Torque is a vector quantity with SI unit Nm [53](#page=53). * **Moment of Inertia (I):** A measure of an object's resistance to changes in its angular velocity. For a single point mass $m$ at a distance $r$ from the axis of rotation: $I = mr^2$ [54](#page=54). For a system of particles, the total moment of inertia is the sum of individual moments of inertia: $I = \sum m_i r_i^2$ [54](#page=54). The SI unit of moment of inertia is kgm$^2$ [54](#page=54). * **Torque and angular acceleration:** The relationship is analogous to Newton's second law ($F=ma$): $\tau_{\text{net}} = I \alpha$ [55](#page=55). > **Example 2.15:** Three forces act on a body pivoted at O. $F_1 = 10 \, \text{N}$ at $8.0 \, \text{m}$ (120$^\circ$), $F_2 = 16 \, \text{N}$ at $4.0 \, \text{m}$ (150$^\circ$), and $F_3 = 19 \, \text{N}$ at $3.0 \, \text{m}$ (45$^\circ$). > Net torque about O: $\tau_{\text{net}} = -r_1 F_1 \sin(120^\circ) + r_2 F_2 \sin(150^\circ) + r_3 F_3 \sin(45^\circ)$ > $\tau_{\text{net}} \approx -69.3 \, \text{Nm} + 32 \, \text{Nm} + 40.3 \, \text{Nm} \approx 3 \, \text{Nm}$ (counterclockwise) [54](#page=54). > **Example 2.16:** Three particles with masses 4 kg, 2 kg, and 3 kg are connected by rods along the y-axis and rotate about the x-axis. > Moment of inertia about the x-axis: $I = (4 \, \text{kg})(3 \, \text{m})^2 + (2 \, \text{kg})(-2 \, \text{m})^2 + (3 \, \text{kg})(-4 \, \text{m})^2 = 164 \, \text{kgm}^2$ [55](#page=55). > **Example 2.17:** A torque of 36 Nm applied to a wheel results in an angular acceleration of 24 rad/s$^2$. > Rotational inertia: $I = \frac{\tau}{a} = \frac{36 \, \text{Nm}}{24 \, \text{rad/s}^2} = 1.5 \, \text{kgm}^2$ [55](#page=55). ### 2.4 Planetary motion and Kepler's Laws Kepler's laws describe the motion of planets orbiting the Sun [57](#page=57). * **Kepler's First Law (Law of Ellipses):** The orbit of a planet about the Sun is an ellipse with the Sun at one focus [58](#page=58). * **Kepler's Second Law (Law of Equal Areas):** An imaginary line drawn from the Sun to a planet sweeps out equal areas in equal time intervals. This means a planet moves fastest when closest to the Sun (perihelion) and slowest when furthest (aphelion) [58](#page=58). * **Kepler's Third Law (Law of Harmonies):** The ratio of the square of a planet's orbital period ($T$) to the cube of its average orbital radius ($R$) is constant for all planets orbiting the same central body: $\frac{T^2}{R^3} = K$ [59](#page=59). The constant $K$ is independent of the planet's mass [59](#page=59). > **Example 2.19:** Earth's orbital period is 365 days, and its mean distance from the Sun is $1.495 \times 10^8 \, \text{km}$. Pluto's mean distance is $5.896 \times 10^9 \, \text{km}$. > Pluto's orbital period: $\frac{T_E^2}{R_E^3} = \frac{T_P^2}{R_P^3} \implies T_P = T_E \sqrt{\frac{R_P^3}{R_E^3}} \approx 9.0 \times 10^4 \, \text{days}$ [60](#page=60). > **Example 2.20:** Saturn is 9 times farther from the Sun than Earth. > Saturn's year in terms of Earth years: $\frac{T_E^2}{R_E^3} = \frac{T_S^2}{R_S^3} \implies T_S = T_E \sqrt{\left(\frac{R_S}{R_E}\right)^3} = (1 \, \text{year}) \sqrt{9^3} = 27 \, \text{years}$ [60](#page=60). ### 2.5 Newton’s law of Universal Gravitation Newton's law of universal gravitation describes the attractive force between any two masses in the universe. * **Gravitational Force ($F_g$):** The force of attraction between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers: $F_g = G \frac{m_1 m_2}{r^2}$ [62](#page=62). where $G$ is the universal gravitational constant, approximately $6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$. The force is always attractive and directed along the line joining the two masses [62](#page=62). * **Gravitational acceleration ($g$):** This law also explains the acceleration due to gravity at Earth's surface. By equating $F_g = mg$ with Newton's law of gravitation: $mg = G \frac{M_E m}{r_E^2} \implies g = G \frac{M_E}{r_E^2}$ [63](#page=63). The calculated value of $g$ using Earth's mass ($M_E$) and radius ($r_E$) is approximately $9.8 \, \text{m/s}^2$ [63](#page=63). * **Centripetal Force:** The gravitational force provides the centripetal force necessary to keep planets in orbit. For a planet of mass $m_p$ orbiting the Sun of mass $M_s$ at radius $r$ with speed $v$: $F_c = \frac{m_p v^2}{r} = G \frac{M_s m_p}{r^2}$ [64](#page=64). This leads to the orbital speed $v = \sqrt{\frac{GM_s}{r}}$. Using $v = \frac{2\pi r}{T}$, we can derive Kepler's third law [64](#page=64): $\frac{T^2}{r^3} = \frac{4\pi^2}{GM_s} = K$ [64](#page=64). > **Example 2.21:** Calculate the force of attraction between a 10 kg mass and a 100 kg mass that are 1 meter apart. > $F_g = (6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2) \frac{(10 \, \text{kg})(100 \, \text{kg})}{(1 \, \text{m})^2} = 6.67 \times 10^{-8} \, \text{N}$ [62](#page=62). > **Example 2.22:** Calculate the gravitational force on a 60.0 kg person at Earth's surface. > $F_g = (6.673 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2) \frac{(5.97 \times 10^{24} \, \text{kg})(60 \, \text{kg})}{(6.38 \times 10^6 \, \text{m})^2} \approx 584 \, \text{N}$ [63](#page=63). --- # Fluid mechanics Fluid mechanics is the study of the behavior of fluids at rest and in motion [70](#page=70). ### 3.1 Fluid statics Fluid statics deals with fluids at rest, which can be either gaseous or liquid. When a fluid is at rest, there is no relative motion between adjacent fluid layers, meaning no shear stresses exist. The primary stress considered in fluid statics is normal stress, known as pressure, which varies due to the fluid's weight. Fluid statics is significant in gravity fields, with force relations involving gravitational acceleration ($g$). Forces exerted by a fluid at rest on a surface are normal to the surface because there are no shear forces parallel to it [73](#page=73). #### 3.1.1 Properties of solids, liquids, and gases * **Solids:** Atoms are in close contact, held by strong forces that allow vibration but prevent position changes. They resist all types of stress and compression due to their fixed lattice structure [71](#page=71). * **Liquids:** Molecules are in close contact but can slide over each other. Intermolecular forces are weaker than in solids but stronger than in gases. Liquids deform easily under stress and do not return to their original shape due to free-moving molecules. Liquids maintain their volume but take the shape of their container [71](#page=71) [72](#page=72). * **Gases:** Atoms are widely separated, with weak intermolecular forces except during collisions. Gases flow easily and are compressible due to the large space and weak forces between atoms. Gases expand to fill the entire available space of their container [71](#page=71) [72](#page=72). > **Tip:** Activity 3.1 demonstrates the compressibility difference between gases and liquids using syringes [72](#page=72). #### 3.1.2 Pressure in fluid Pressure is defined as a normal force exerted by a fluid (or solid) per unit area. It is calculated as $P = \frac{F}{A}$, where $F$ is the force magnitude and $A$ is the contact area. Pressure is a scalar quantity [74](#page=74). * **Units of Pressure:** * SI unit: newtons per square meter (N/m²), also known as pascal (Pa) [74](#page=74). * Other units: millimeter mercury (mmHg), torr, atmosphere (atm), pounds per square inch (psi) [74](#page=74). * Conversions: 1 atm = 760 mmHg = 760 torr = 101.3 kPa = 14.7 psi [75](#page=75). > **Example:** A woman's weight exerts pressure on the floor through her shoe. Calculating this pressure and converting it to other units demonstrates the relationship between force, area, and pressure. Example 3.1 calculates pressure exerted by a shoe. Example 3.3 shows how nail tips exert tremendous pressure due to a large force over a small area [75](#page=75) [76](#page=76). #### 3.1.3 Pressure in gases Pressure in gases is formed by the constant bombardment of gas particles colliding with solid surfaces. Each collision exerts an impulsive force, and the collective effect of a huge number of particles colliding at a constant rate results in an approximately constant force and thus pressure. Increasing the number of gas particles in a container increases the collision rate and the outward force, causing expansion [76](#page=76) [77](#page=77). * **Absolute Pressure ($P_{abs}$):** The actual pressure at a given position, measured relative to absolute vacuum (zero pressure) [77](#page=77). * **Gauge Pressure ($P_{gauge}$):** The difference between absolute pressure and local atmospheric pressure. Pressure gauges are often calibrated to read zero in the atmosphere. $P_{gauge} = P_{abs} - P_{atm}$ [77](#page=77) [78](#page=78). * **Vacuum Pressure ($P_{vac}$):** Pressures below atmospheric pressure are sometimes called vacuum pressures. Vacuum gauges indicate the difference between atmospheric pressure and absolute pressure. $P_{vac} = P_{atm} - P_{abs}$ [77](#page=77) [78](#page=78). > **Tip:** Understanding the relationship between absolute, gauge, and vacuum pressure is crucial for many fluid mechanics problems. Figure 3.7 illustrates these relationships. Example 3.4 demonstrates calculating absolute pressure using vacuum and atmospheric pressure [77](#page=77) [78](#page=78) [79](#page=79). #### 3.1.4 Density Density ($\rho$) is defined as mass ($m$) per unit volume ($V$) [80](#page=80): $$ \rho = \frac{m}{V} \quad (3.5) $$ The SI unit for density is kg/m³. Density is crucial for determining if an object sinks or floats and directly affects fluid pressure [79](#page=79) [80](#page=80). * **Gases:** Density is generally proportional to pressure and inversely proportional to temperature [80](#page=80). * **Liquids and Solids:** Density variation with pressure is usually negligible as they are essentially incompressible [80](#page=80). **Table 3.1: Densities of some common substances** (Selected entries) [81](#page=81). | Substance | $\rho$ (kg/m³) | Substance | $\rho$ (kg/m³) | | :------------- | :--------------- | :-------- | :------------- | | Air | $1.29 \times 10^3$ | Iron | $7.86 \times 10^3$ | | Aluminum | $2.70 \times 10^3$ | Lead | $11.3 \times 10^3$ | | Fresh water | $1.00 \times 10^3$ | Mercury | $13.6 \times 10^3$ | | Sea water | $1.03 \times 10^3$ | Gold | $19.3 \times 10^3$ | > **Tip:** Density helps identify material composition and phase. Example 3.6 calculates the density of a person [80](#page=80). #### 3.1.5 Specific gravity Specific gravity (SG), or relative density, is the ratio of the density of a substance to the density of a standard substance (usually water at 4°C, where $\rho_{H_2O} = 1000$ kg/m³) [81](#page=81): $$ SG = \frac{\rho}{\rho_{H_2O}} $$ Specific gravity is a dimensionless quantity. Substances with SG less than 1 are less dense than water and will float on it [81](#page=81) [82](#page=82). > **Tip:** The ideal-gas equation of state relates density and pressure for gases: $P = \rho \frac{R}{M} T$. Example 3.7 calculates the density, specific gravity, and mass of air in a room [82](#page=82). ### 3.2 Properties of pressure in fluids This section explores how pressure behaves in fluids, including Pascal's law, pressure variations with depth, and pressure-measuring devices [84](#page=84). #### 3.2.1 Pascal's law Pascal's law states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every point within the fluid and to the walls of the container. This means an increase in pressure at one location causes a uniform pressure increase throughout the fluid [85](#page=85). * **Microscopic explanation:** When pressure is applied to a surface, fluid molecules near that surface collide more frequently with their neighbors, propagating the increased pressure throughout the fluid [85](#page=85). > **Tip:** Activity 3.3 demonstrates how pressure is exerted in all directions in a liquid. Activity 3.4 shows pressure transmission in connected syringes [84](#page=84) [86](#page=86). #### 3.2.2 Hydraulic lift Hydraulic lifts are practical applications of Pascal's law that convert small forces into larger ones. They work by applying a force ($F_1$) to a small piston with area ($A_1$), creating pressure ($P_1 = \frac{F_1}{A_1}$). This pressure is transmitted equally to a larger piston with area ($A_2$), resulting in a larger upward force ($F_2 = P_1 A_2$) [86](#page=86): $$ F_2 = \frac{A_2}{A_1} F_1 \quad (3.8) $$ This force multiplication allows for lifting heavy objects like cars [87](#page=87). > **Tip:** While hydraulic systems multiply force, the work done remains the same: $F_1 d_1 = F_2 d_2$. Example 3.8 illustrates the force multiplication in a hydraulic lift [87](#page=87) [88](#page=88). #### 3.2.3 Variation of pressure with depth In a fluid at rest with uniform density ($\rho$), the pressure ($P$) at a depth ($h$) below a point where the pressure is ($P_0$) is given by: $$ P = P_0 + \rho g h \quad (3.9) $$ where $g$ is the acceleration due to gravity. If the fluid is open to the atmosphere, $P_0$ is the atmospheric pressure ($P_{atm}$) [89](#page=89). * Pressure is the same at all points with the same depth, regardless of the container's shape [90](#page=90). * For gases, this equation is applicable as long as density changes are small over the depth [90](#page=90). > **Tip:** Activity 3.5 demonstrates how the distance water shoots from a bottle varies with the height of the water level, illustrating pressure dependence on depth. Activity 3.6 shows liquid pressure is independent of container shape. Example 3.9 calculates the force on an area at a certain depth in the ocean [89](#page=89) [90](#page=90). #### 3.2.4 Atmospheric pressure Atmospheric pressure is the pressure exerted by the weight of the air above a given location. It decreases with increasing altitude due to two main factors [91](#page=91): 1. **Density:** Gas molecules are denser near the Earth's surface, leading to more collisions and higher pressure [92](#page=92). 2. **Depth of Atmosphere:** The atmospheric depth is greatest at sea level and decreases with altitude, meaning more air presses down from above at lower elevations [92](#page=92). Atmospheric pressure at sea level is approximately 101.325 kPa and decreases significantly at higher altitudes [92](#page=92). > **Tip:** Reduced atmospheric pressure at high altitudes affects cooking times, boiling points, and oxygen availability. Activity 3.7 and 3.8 explore pressure changes related to cooling and sealed containers [92](#page=92). #### 3.2.5 Measuring pressure Several instruments are used to measure pressure: * **Barometer:** Measures atmospheric pressure. A mercury barometer works on the principle that atmospheric pressure supports a column of mercury. The atmospheric pressure ($P_{atm}$) is given by $P_{atm} = \rho g h$ [93](#page=93). * Standard atmosphere (atm): Defined as the pressure exerted by a column of mercury 760 mm high at 0°C [94](#page=94). * Units: mmHg and torr are also used, with 1 atm = 760 torr [94](#page=94). > **Tip:** The length or cross-sectional area of the tube does not affect the height of the fluid column in a barometer (provided capillary effects are negligible). Example 3.10 calculates atmospheric pressure from a barometric reading. Exercise 3.5 explores barometric readings and the height of an oil column in a barometer [93](#page=93) [94](#page=94). * **Manometer:** Measures the pressure of a gas trapped in a container [94](#page=94). * **Closed-end manometer:** Measures gas pressure directly. $P_{gas} = \rho g h$ [95](#page=95). * **Open-end manometer:** Has one arm open to the atmosphere. The difference in liquid levels corresponds to the pressure difference between the gas and the atmosphere [95](#page=95). * $P_{gas} = P_{atm} + \rho g h$ (if the mercury level is higher above the gas-connected arm) * $P_{gas} = P_{atm} - \rho g h$ (if the mercury level is higher above the open arm) > **Tip:** The cross-sectional area of the manometer tube does not affect the differential height ($h$). Example 3.11 calculates absolute pressure using an open manometer [95](#page=95). ### 3.3 Archimedes principle Archimedes' principle deals with the buoyant force exerted by a fluid on an immersed object [96](#page=96). #### 3.3.1 Buoyant force The upward force exerted by a fluid on any immersed object is called the buoyant force ($F_B$). This force arises because pressure increases with depth, so the upward force on the bottom of an object is greater than the downward force on its top [96](#page=96). * **Archimedes' Principle:** The buoyant force on an object equals the weight of the fluid it displaces [97](#page=97). $$ F_B = W_{fluid \: displaced} $$ $$ F_B = \rho_{fluid} g V_{displaced} \quad (3.12) $$ $$ F_B = M_{displaced} g \quad (3.13) $$ > **Tip:** Activity 3.9 explores buoyancy with an egg in salt water and measuring buoyant force [99](#page=99). #### 3.3.2 Totally submerged objects For a totally submerged object, the volume of displaced fluid ($V_{displaced}$) equals the object's volume ($V_{obj}$). The net force on the object is $F_B - F_g = (\rho_{fluid} - \rho_{obj}) g V_{obj}$ [97](#page=97). * If $\rho_{obj} < \rho_{fluid}$, the object floats upwards [97](#page=97). * If $\rho_{obj} > \rho_{fluid}$, the object sinks [97](#page=97). * If $\rho_{obj} = \rho_{fluid}$, the object remains suspended [97](#page=97). #### 3.3.3 Floating objects When an object floats, it is partially submerged. The buoyant force balances the object's weight ($F_g = M_{obj} g = \rho_{obj} g V_{obj}$) [98](#page=98): $$ F_B = \rho_{fluid} g V_{displaced} $$ Equating buoyant force and weight: $$ \rho_{fluid} g V_{displaced} = \rho_{obj} g V_{obj} $$ $$ \frac{V_{displaced}}{V_{obj}} = \frac{\rho_{obj}}{\rho_{fluid}} \quad (3.14) $$ This means the fraction of the object's volume submerged is equal to the ratio of its density to the fluid's density [98](#page=98). > **Tip:** This principle explains why icebergs float with a large portion submerged. Example 3.12 calculates the submerged fraction of an iceberg. Example 3.13 calculates the buoyant force on submerged steel and the maximum buoyant force for a boat hull. Example 3.14 determines the density of an ancient coin using apparent mass loss in water [100](#page=100) [98](#page=98). ### 3.4 Fluid flow Fluid flow occurs due to pressure differences, with fluid moving from higher to lower pressure regions . #### 3.4.1 Types of fluid flow * **Steady (Laminar) Flow:** Each fluid particle follows a smooth path, and paths of different particles do not cross. Fluid particles arriving at a point have the same velocity. This occurs at low velocities and in small diameter pipes . * **Turbulent Flow:** Irregular flow characterized by whirlpool-like regions where adjacent layers cross and move randomly. This occurs at high velocities and in larger diameter pipes . > **Tip:** Viscosity is the internal friction in a fluid that causes kinetic energy to be transformed into internal energy during flow. Streamlines represent the path of a fluid particle in steady flow, with velocity tangent to the streamline . #### 3.4.2 Flow rate and equation of continuity * **Flow Rate ($Q$):** The volume of fluid passing a location through an area per unit time . $$ Q = \frac{V}{t} \quad (3.15) $$ The SI unit for flow rate is m³/s . * **Equation of Continuity:** For an incompressible fluid, the flow rate is constant throughout a pipe of varying cross-sectional area . $$ Q_1 = Q_2 $$ $$ A_1 v_1 = A_2 v_2 \quad (3.16) $$ where $A$ is the cross-sectional area and $v$ is the average fluid speed . > **Tip:** This equation relates the cross-sectional area and average speed of incompressible fluid flow. Example 3.15 calculates the volume of blood pumped by the heart over a lifetime. Example 3.16 calculates water speed in a hose and nozzle using the equation of continuity. Discussion 3.5 and 3.6 relate fluid flow to everyday experiences like hoses and paper flying upwards when blown across . #### 3.4.3 Bernoulli's principle Bernoulli's principle states that the pressure exerted by a moving fluid decreases as the speed of the fluid increases. This principle has applications in understanding phenomena like snoring and the lift on airplane wings . ### 3.5 Safety and high pressure High pressure is defined as pressure significantly greater than 1 atmosphere (often greater than 50 atm). High-pressure systems have numerous applications but also pose significant safety risks if not managed properly . #### 3.5.1 Applications of high-pressure systems High pressure is utilized in: * Kitchen appliances (high-pressure cookers) . * Fuel sources (gas cylinders containing LPG) . * Laboratory and medical uses (compressed gas cylinders) . * Vehicle inflation (bicycle and car tires) . * Cleaning equipment (high-pressure washers) . * Scientific research (studying material properties) . * Food preservation (pascalization) . #### 3.5.2 Components of high-pressure equipment High-pressure equipment may include: * High-pressure compressors (or pumps) . * High-pressure piping (fittings, seals, tubing, valves) . * High-pressure vessels . * Safety accessories (safety valves, bursting discs) . * High-pressure instrumentation (for measurement and control) . #### 3.5.3 Safety measures for high-pressure systems Failure of pressure systems can cause serious injury and damage due to blast impact, flying debris, or released liquids/gases. Common causes of risks include damaged equipment, poor maintenance, operator error, and incorrect installation . * **High Pressure Gas Cylinders:** Should be kept upright, in ventilated areas, protected from impact, away from flammable materials, and knobs should be turned off after use . * **High Pressure Washers:** Require safety glasses, enclosed shoes, gloves, and ear protection. Never point the washer at people or pets, and always turn off the machine before disconnecting hoses . > **Tip:** Always follow manufacturer instructions and proper safety protocols when operating high-pressure equipment . --- # Electromagnetism Electromagnetism unifies the phenomena of electricity and magnetism, describing how they interact and influence each other. ## 4 Electromagnetism Electromagnetism is a fundamental force in nature that describes the interaction between electrically charged particles and magnetic fields, leading to phenomena like electromagnetic fields and the operation of devices such as electromagnets . ### 4.1 Magnets and magnetic fields A magnet generates a magnetic field, which is the region around the magnet where magnetic forces are exerted. Magnetic poles are the parts of a magnet that exert the strongest force; every magnet has a north (N) and a south (S) pole. Like poles repel, and opposite poles attract. Unlike electric charges, magnetic poles cannot be isolated; they always exist in pairs . There are two main types of magnets: * **Permanent magnets:** These materials generate their magnetic field from their internal structure and retain their magnetism for extended periods . * **Electromagnets:** These are typically coils of wire that produce a magnetic field when an electric current flows through them and lose their magnetism when the current is switched off. An iron core can be used to increase the strength of an electromagnet . The Earth itself possesses a magnetic field, behaving like a giant bar magnet, with its magnetic poles roughly aligned with the geographic poles . A magnetic field is the region around a magnet or a moving electric charge where magnetic forces act. It is a vector quantity, and its direction is indicated by where a compass needle would point . **Differences between electric and magnetic fields:** * **Units:** The SI unit for electric field is Newton/coulomb, while for magnetic field, it is Tesla (T) . * **Source:** Electric fields are produced by electric charges, while magnetic fields are produced by dipoles (north and south poles) . * **Field Lines:** Electric field lines originate from positive charges and terminate on negative charges. Magnetic field lines, however, do not have distinct starting or ending points and form closed loops . ### 4.2 Magnetic field lines Magnetic field lines are imaginary lines used to visualize magnetic fields. Their density indicates the field's magnitude. When iron filings are sprinkled around a magnet, they align themselves along these lines, revealing the magnetic field pattern . **Properties of magnetic field lines:** * They indicate both the direction (tangent to the line) and magnitude (density) of the magnetic field at any point . * Magnetic field lines never cross, ensuring a unique field at each point . * They form continuous, closed loops without beginnings or ends, emerging from the north pole and merging into the south pole, and continuing internally from south to north . Figure 4.6 illustrates a comparison between magnetic and electric field lines . ### 4.3 Current and magnetism An electric current flowing through a conductor produces a magnetic field. This principle is fundamental to the operation of electromagnets. The presence of this magnetic field can be demonstrated by observing the deflection of a compass needle placed near a current-carrying wire. When the current is switched off, the magnetic field disappears because it is generated by the movement of electric charges . **Ampere's law** states that the magnetic field around an electric current is proportional to the current, and the total field is the vector sum of the fields produced by each segment of the current . #### Magnetic field created by a long straight current-carrying wire For a long straight wire, the magnitude of the magnetic field ($B$) is given by: $$B = \frac{\mu_0 I}{2\pi r}$$ . where: * $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \text{ T}\cdot\text{m/A}$) . * $I$ is the current in the wire . * $r$ is the shortest distance from the wire . The SI unit for magnetic field is the Tesla (T). A non-SI unit, the gauss (G), is also used, with $1 \text{ T} = 10^4 \text{ G}$ . **Characteristics of the magnetic field around a straight wire:** * The field lines form a circular pattern around the wire . * The magnetic field strength increases with increasing current . * The field is stronger closer to the wire and weaker further away . * Reversing the direction of the current reverses the direction of the magnetic field . The direction of the magnetic field around a straight current-carrying wire is determined by **Fleming's Right Hand Rule**. If you grip the wire with your right hand such that your thumb points in the direction of the current, your fingers curl in the direction of the magnetic field lines . **Activity 4.1:** This activity guides students to build a simple electromagnet and observe the magnetic effects of current . **Example 4.1:** Calculates the current in a wire producing a magnetic field twice the strength of Earth's magnetic field at a specific distance . Amperes's law is crucial in the manufacturing of various electrical machines like motors, generators, and transformers . **Table 4.1:** Lists approximate magnitudes of magnetic fields from various sources . An electromagnet is a temporary magnet created by electric current, widely used in devices like electric bells, motors, generators, and MRI machines . **Magnetic Relays:** These are magnetically activated switches. A reed relay uses two nickel-iron blades that attract and close a circuit when a magnetic field is applied . **Electric Bell:** The operation of an electric bell relies on an electromagnet that repeatedly attracts and releases a hammer to strike the bell . **DC Electric Motor:** Electric motors operate on the principle that a current-carrying loop placed in a magnetic field experiences a torque, causing it to rotate continuously . ### 4.4 Electromagnetic induction Electromagnetic induction is the process where a changing magnetic field induces an electromotive force (emf) and, consequently, an electric current in a conductor. Michael Faraday's experiments in 1831 demonstrated that a changing magnetic field could generate electricity, leading to the invention of the dynamo (generator) . **Activity 4.2:** This activity demonstrates electromagnetic induction by moving a magnet near a coil connected to a galvanometer, observing deflections that indicate induced current. The magnitude of the induced voltage is proportional to the speed of movement between the coil and the magnetic field . #### Magnetic flux Magnetic flux ($\Phi_B$) is a measure of the total magnetic field lines passing through a given area. For a flat surface area $A$ in a uniform magnetic field $B$, it is calculated as : $$\Phi_B = \vec{B} \cdot \vec{A} = BA \cos \theta$$ . where $\theta$ is the angle between the magnetic field vector ($\vec{B}$) and the area vector ($\vec{A}$) . **Example 4.2:** Calculates the magnetic flux through a square loop positioned at an angle to a magnetic field . ### 4.5 Faraday's law of electromagnetic induction Faraday's experiments revealed that induced current is produced when there is relative motion between a coil and a magnet, and the direction of the current depends on the pole of the magnet and the direction of motion . **Faraday's laws of electromagnetic induction:** 1. **Faraday's Law:** The magnitude of the induced electromotive force (emf, $\varepsilon$) in a closed coil is directly proportional to the rate of change of magnetic flux ($\Delta\Phi_B$) through the coil over a time interval ($\Delta t$) . $$\varepsilon = -\frac{\Delta\Phi_B}{\Delta t}$$ . For a coil with $N$ turns, the total induced emf is: $$\varepsilon = -N \frac{\Delta\Phi_B}{\Delta t}$$ . The induced emf can be increased by increasing the number of turns ($N$), or by changing the magnetic field strength ($B$), area ($A$), or the angle ($\theta$) . **Example 4.3:** Determines the induced emf and current in a square loop as the magnetic field decreases over time . 2. **Lenz's Law:** This law states that an induced current always flows in a direction that opposes the change in magnetic flux that produced it. This principle is derived from the conservation of energy and is reflected by the negative sign in Faraday's law . **Figure 4.15:** Illustrates how Lenz's Law dictates the direction of induced current based on the approaching pole of a magnet . ### 4.6 Transformers A transformer is an electrical device that transfers electrical energy from one circuit to another through electromagnetic induction. It is used to increase ('step up') or decrease ('step down') voltage levels between circuits without changing the frequency . A transformer consists of two coils (primary and secondary) wound on a common core, often made of iron. The alternating current in the primary coil creates a changing magnetic flux that induces an emf in the secondary coil via mutual induction . The ratio of the number of turns in the primary coil ($N_p$) to the number of turns in the secondary coil ($N_s$) determines the voltage transformation: $$\frac{N_p}{N_s} = \frac{V_p}{V_s} = \text{Turns Ratio}$$ . where $V_p$ and $V_s$ are the primary and secondary voltages, respectively . Transformers can be highly efficient, often reaching 98% . $$\text{efficiency}, \eta = \frac{\text{output power}}{\text{input power}} \times 100\%$$ . **Example 4.4:** Calculates the output voltage of a transformer given the number of turns and input voltage . Transformers are essential in household appliances like phone chargers, laptop power supplies, and microwaves, stepping down high voltages from the power grid to safe levels for electronic devices or stepping them up for specific functions . ### 4.7 Application and safety Electromagnetism and electromagnetic induction have numerous daily applications. Computer hard drives, graphics tablets, and credit card readers utilize principles of magnetism and induction . **Applications of magnets in real life:** * Electric bells . * Generators and electric motors . * Navigation (compasses) . * Separation of magnetic and non-magnetic materials . * Medical treatments for pain . **Electric, Magnetic, and Electromagnetic Field Safety:** These fields are classified as non-ionizing radiation. Safety guidelines differ from ionizing radiation . **Safety tips for using electromagnets:** 1. Define the type and characteristics of the plates to be lifted . 2. Check for potential environmental hazards, such as active body implants that can be affected by electromagnetic fields . 3. Perform regular overhauls and checks of the electromagnet and lifting system before use . 4. Select the electromagnet that is most suitable for the specific project's requirements . --- # Basics of electronics This unit introduces fundamental concepts in electronics, covering semiconductors, diodes, transistors, integrated circuits, and logic gates, along with their applications . ### 5.1 Semiconductors Semiconductors are materials with conductivity between conductors and insulators, playing a crucial role in modern electronic components . #### 5.1.1 Conductors, Insulators, and Semiconductors * **Conductors:** Materials that allow electricity to flow through them, possessing free electrons that facilitate current flow. Metals are good conductors . * **Insulators:** Materials that do not allow electricity to pass through them, as their electrons are tightly bound to the atom. Examples include plastic, wood, glass, and rubber . * **Semiconductors:** Materials with conductivity between conductors and insulators. They can be pure elements like silicon (Si) or germanium (Ge), or compounds like gallium arsenide . * At absolute zero temperatures, semiconductors act as insulators . * At higher temperatures, conduction occurs as electrons break free from covalent bonds and move freely . #### 5.1.2 Semiconductor Lattice Structure Semiconductors like Silicon (Si) have atoms bonded in a regular, periodic structure . * Each atom is surrounded by eight electrons, typically involved in covalent bonds . * A **covalent bond** involves two atoms sharing a pair of electrons. Each atom forms four covalent bonds with surrounding atoms . * **Hole:** An electric charge carrier with a positive charge, equal in magnitude but opposite in polarity to an electron. It represents the absence of an electron in a specific location within the atomic lattice. Holes are key charge carriers responsible for current in semiconductors . #### 5.1.3 Types of Semiconductors Semiconductors are classified into intrinsic and extrinsic types . ##### 5.1.3.1 Intrinsic Semiconductor * Composed of only one type of material, such as pure silicon or germanium . * Also known as undoped semiconductors, as no impurities have been added to alter carrier concentrations . ##### 5.1.3.2 Extrinsic Semiconductor * Created by adding controlled amounts of impurities (dopants) to pure semiconductors to significantly improve conductivity . * **Doping:** The process of adding impurities to a pure semiconductor crystal to enhance its conductivity . * The goal of doping is to create an excess (surplus) or deficiency of electrons . * Extrinsic semiconductors are further classified into N-type and P-type . ###### 5.1.3.2.1 N-Type Semiconductor * Created by adding an element with more valence electrons than the intrinsic semiconductor, typically from Group V of the periodic table (e.g., antimony, arsenic, bismuth, phosphorus) . * These elements have five valence electrons, one more than Group IV elements like silicon . * Conduction primarily occurs through electron flow . * **Majority charge carriers:** Electrons . * **Minority charge carriers:** Holes . * Dopant atoms that donate free electrons are called **donor atoms** . * For example, silicon doped with arsenic (As). The fifth valence electron of As is free to move for conduction . ###### 5.1.3.2.2 P-Type Semiconductor * Created by adding a Group III element (e.g., aluminum, boron, gallium, indium) to a pure semiconductor . * These elements have three valence electrons, creating a deficiency of electrons in the covalent bonds . * This deficiency creates a **hole**, which acts as a positive charge carrier . * **Majority charge carriers:** Holes . * **Minority charge carriers:** Electrons . * Dopant atoms that accept electrons are called **acceptor atoms** . * For example, silicon doped with boron. Boron needs one more electron to complete its covalent bond, thus creating a hole . ### 5.2 Diodes and their functions A diode is a two-terminal electronic component that allows current to flow in only one direction . #### 5.2.1 P-N Junction Diode * Formed by joining an n-type semiconductor with a p-type semiconductor . * **Symbol:** An arrow pointing from anode (p-side) to cathode (n-side), indicating the direction of conventional current flow . * **Formation:** When joined, electrons from the n-region diffuse to the p-region and combine with holes, leaving positive ions in the n-region and negative ions in the p-region . * **Depletion Region:** A narrow region near the junction with very few mobile charge carriers (electrons and holes) . * **Barrier Potential:** An electric field created by the ions in the depletion region that opposes further diffusion . * For silicon, the barrier potential is approximately 0.7V . * For germanium, the barrier potential is approximately 0.3V . #### 5.2.2 Biasing of P-N Junction Diode Applying a DC voltage to a diode is called biasing . ##### 5.2.2.1 Forward Bias * **Connection:** The positive terminal of the battery is connected to the p-type semiconductor (anode), and the negative terminal to the n-type semiconductor (cathode) . * **Effect:** Electrons and holes move towards the junction, repelled by the battery terminals. This decreases the width of the depletion region and reduces the potential barrier . * **Conduction:** The diode conducts electricity, and current increases with increasing battery voltage . ##### 5.2.2.2 Reverse Bias * **Connection:** The negative terminal of the battery is connected to the p-type semiconductor (anode), and the positive terminal to the n-type semiconductor (cathode) . * **Effect:** Holes in the p-type material are pulled away from the junction, and electrons in the n-type material are also pulled away from the junction. This increases the width of the depletion region and the potential barrier . * **Conduction:** High resistance to charge carrier flow results in no significant current flow through the junction . * **Breakdown Voltage:** At a sufficiently high reverse bias voltage, current increases very rapidly . #### 5.2.3 Current-Voltage Characteristics * **Forward Bias:** Current increases slowly and non-linearly. Once the external voltage exceeds the barrier voltage, the diode behaves like a conductor, and the current rises sharply . * **Reverse Bias:** A small current (leakage current) flows due to minority carriers. Beyond the breakdown voltage, a sharp increase in reverse current occurs . #### 5.2.4 Practical Uses of Diodes * **Rectification:** Converting alternating current (AC) to direct current (DC) . * **Light Emitting Diodes (LED):** Emit light when current flows in the forward direction due to electron-hole recombination releasing energy as photons . * **Photodiode:** Converts photons (light) into an electrical current when light is absorbed in the depletion region, creating electron-hole pairs . * **Logic Gates:** Can be combined with other components to form AND and OR logic gates (diode logic) . * **Over-voltage Protection:** Diodes can shut down a converter in response to overvoltage conditions to protect sensitive devices . ### 5.3 Rectification Rectification is the process of converting AC voltage into unidirectional (DC) voltage using a rectifier circuit . #### 5.3.1 Half-wave Rectifier * Allows only one half-cycle of an AC waveform to pass, blocking the other . * Consists of a diode and a load resistor in series . * During the positive half-cycle, the diode is forward-biased, and current flows through the load . * During the negative half-cycle, the diode is reverse-biased, and no current flows . * Output is a pulsating DC signal . #### 5.3.2 Full-wave Rectifier * Utilizes all half-cycles of the AC input to produce a DC output, overcoming the inefficiency of half-wave rectification . * A common configuration is the bridge rectifier, requiring four diodes . * **Working Principle:** During the positive half-cycle, two diodes conduct, passing current through the load. During the negative half-cycle, the other two diodes conduct, ensuring current flows through the load in the same direction . * Output is a pulsating DC signal with a higher frequency than the half-wave rectifier . #### 5.3.3 Diodes and Capacitors in Rectifiers * Capacitors are used in rectifier circuits to smooth the output voltage fluctuations . * A capacitor charges during the peak voltage and discharges to supply current to the load as the voltage falls, smoothing the waveform . ### 5.4 Transistors and their application Transistors are essential components used for amplification or switching in electronic circuits . #### 5.4.1 Types of Transistors * **Bipolar Junction Transistors (BJT):** Operate based on the flow of both electrons and holes . * **Field-Effect Transistors (FET):** Operate based on the control of an electric field. This section focuses on BJTs . #### 5.4.2 Bipolar Junction Transistors (BJT) * A three-terminal, two-junction device used to control electron flow . * By varying voltage at the terminals, current can be controlled . * **Construction:** Consists of three alternately doped semiconductor regions: * **NPN Transistor:** A p-type layer sandwiched between two n-type layers . * **PNP Transistor:** An n-type layer sandwiched between two p-type layers . * **Regions:** * **Emitter (E):** Supplies charge carriers (heavily doped) . * **Collector (C):** Collects charge carriers (moderately doped) . * **Base (B):** The thin middle section that controls current flow (lightly doped and very thin) . * **Symbol:** The arrow on the emitter indicates the direction of conventional current flow. For NPN, the arrow points outward; for PNP, it points inward . #### 5.4.3 Basic Transistor Operation (NPN Example) * **Biasing:** For proper operation, the emitter-base junction is forward-biased, and the collector-base junction is reverse-biased . * Emitter-base junction: Forward-biased (e.g., emitter to negative, base to positive in NPN) . * Collector-base junction: Reverse-biased (e.g., collector to positive, base to positive but more positive than the base in NPN) . * **Operation:** Electrons are emitted from the emitter, cross the forward-biased junction, and most of them are attracted to the collector due to the reverse bias. A small number of electrons combine with holes in the base, forming the base current . * **Current Relationship:** The emitter current is the sum of the base current and the collector current . $$I_E = I_B + I_C$$ (5.1) . #### 5.4.4 PNP Transistor Operation * Works similarly to NPN, but the majority charge carriers are holes . * Biasing is reversed: Emitter-base junction forward-biased (emitter to positive, base to negative), and collector-base junction reverse-biased (collector to negative) . #### 5.4.5 Transistor Configurations Three configurations allow a transistor to be used in a circuit, with one terminal common to both input and output signals : * **Common Collector:** Input signal applied between base and collector; output taken between emitter and collector. Provides good current gain . * **Common Base:** Input signal applied to the emitter; output taken from the collector. The base is common. Provides good voltage and power gain . * **Common Emitter:** Input signal applied between base and emitter; output taken between collector and emitter. Provides voltage, current, and power gain . * **Current Gain (β):** The ratio of collector current to base current . $$\beta = \frac{I_C}{I_B}$$ . * **Example 5.1:** A transistor with $\beta = 250$ and $I_B = 20$ µA has a collector current $I_C = \beta I_B = 250 \times 20 \, \mu\text{A} = 5$ mA . #### 5.4.6 Output Characteristics of Common Emitter * Describes the relationship between collector current ($I_C$) and collector-emitter voltage ($V_{CE}$) for a constant base current ($I_B$) . * Typically, a small change in base current ($I_B$) results in a much larger change in collector current ($I_C$), indicating amplification . ### 5.5 Integrated Circuits Integrated Circuits (ICs), or chips, are miniaturized electronic circuits fabricated on a single semiconductor substrate . #### 5.5.1 Importance and Advantages * Revolutionized electronics, enabling smaller, more powerful, and more affordable devices . * **Advantages:** * Small size and light weight . * Low power consumption . * High speed due to reduced electron travel time . * Increased reliability due to permanent internal connections and pre-testing . * Economical to produce, reducing manufacturing costs . * Provide new and better solutions to complex problems . #### 5.5.2 Components of an IC * An IC typically consists of diodes, transistors, resistors, and capacitors fabricated on a silicon chip . * Resistors and capacitors occupy more space than diodes and transistors in an IC . #### 5.5.3 Disadvantages of ICs * Cannot handle large amounts of current or voltage, as high current generates heat and high voltage can break down insulation . * Cannot be repaired; if faulty, they must be replaced . ### 5.6 Logic gates and logic circuits Logic gates are fundamental building blocks of digital electronics, performing logical operations on digital signals . #### 5.6.1 Digital and Analog Signals * **Analog Signal:** A continuous signal whose voltage or current varies smoothly over time . * **Digital Signal:** A signal that represents data as a sequence of discrete values. In most digital circuits, it has two possible values: a high state (represented by '1') and a low state (represented by '0') . * **Binary Signal/Logic Signal:** A digital signal with two distinct voltage levels . #### 5.6.2 Positive and Negative Logic * **Positive Logic:** '1' represents a high voltage (On, True), and '0' represents a low voltage (Off, False) . * **Negative Logic:** '0' represents a high voltage (On, True), and '1' represents a low voltage (Off, False) . #### 5.6.3 Basic Logic Gates Logic gates are digital circuits that process input signals according to specific logical rules (Boolean expressions) to produce an output . * **Boolean Expressions:** Mathematical representations of logic gate operations. * Addition (+) represents OR. $y = A + B$ . * Multiplication (.) represents AND. $y = A \cdot B$ . * Bar (-) represents NOT. $y = \overline{A}$ . ##### 5.6.3.1 OR Gate * **Function:** The output is '1' if at least one of its inputs is '1' . * **Boolean Expression:** $y = A + B$ . * **Analogy:** Two parallel switches controlling a lamp. The lamp is ON if either switch is closed . * **Truth Table:** | A | B | Y | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 | * **Application:** Used in circuits where an action should occur if any of multiple conditions are met (e.g., corridor lights controlled by switches at both ends) . ##### 5.6.3.2 AND Gate * **Function:** The output is '1' if and only if all of its inputs are '1' . * **Boolean Expression:** $y = A \cdot B$ . * **Analogy:** Two switches in series controlling a lamp. The lamp is ON only if both switches are closed . * **Truth Table:** | A | B | Y | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | * **Application:** Used in circuits where an action requires multiple conditions to be met simultaneously (e.g., an airplane display lighting up only if both toilets are occupied) . ##### 5.6.3.3 NOT Gate (Inverter) * **Function:** Inverts or complements the input. The output is the opposite of the input . * **Boolean Expression:** $y = \overline{A}$ . * **Analogy:** A single switch controlling a lamp. If the switch is open the lamp is ON; if the switch is closed the lamp is OFF [1](#page=1). * **Truth Table:** | A | Y | |---|---| | 0 | 1 | | 1 | 0 | * **Application:** Used to reverse a logic state (e.g., to turn on a water pipe when soil is dry, given a sensor output that is '0' for dry soil) . #### 5.6.4 Universal Logic Gates * **NAND Gate:** Combination of an AND gate and a NOT gate . * **Boolean Expression:** $Y = \overline{A \cdot B}$ . * **Function:** Output is '0' only when all inputs are '1' . * **Truth Table:** | A | B | Y | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | * **NOR Gate:** Combination of an OR gate and a NOT gate . * **Boolean Expression:** $Y = \overline{A + B}$ . * **Function:** Output is '1' only when all inputs are '0' . * **Truth Table:** | A | B | Y | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 0 | ### 5.7 Application of Electronics Electronics has permeated numerous sectors, simplifying tasks and enabling advanced technologies . * **Aerospace Industry:** Space shuttles, satellites, aircraft systems (measurements, power management) . * **Medical:** Diagnostic equipment (MRI, CT, X-ray), robotic surgery, patient monitoring . * **Automobile:** Engine control units (ECUs), infotainment systems, safety features, driver assistance . * **Utility Systems:** High voltage DC transmission, smart grids, renewable energy integration (solar, wind) . * **Commercial:** Advertising displays, climate control, office equipment, uninterruptible power supplies (UPS) . * **Agriculture:** Crop monitoring sensors, soil analysis, automated irrigation systems . * **Communication:** Acquisition, processing, storage, and transmission of information . * **Industrial:** Industrial furnaces, robotics, control systems in manufacturing, welding . * **Residential:** Home appliances (air conditioners, computers, mobile phones), entertainment systems . * **Military:** Unmanned aerial vehicles (UAVs), drones, targeting systems, surveillance equipment (night vision, infrared detectors) . --- ## Common mistakes to avoid - Review all topics thoroughly before exams - Pay attention to formulas and key definitions - Practice with examples provided in each section - Don't memorize without understanding the underlying concepts

| Term | Definition | |------|------------| | Physics | The branch of science concerned with the nature and properties of matter and energy, and the fundamental forces that govern its behavior. | | Spectroscopy | The study of the interaction between matter and electromagnetic radiation as a function of the wavelength or frequency of the radiation. | | Newtonian mechanics | A description of motion that uses Newton’s laws of motion and gravity to describe how objects move and interact. | | Fluid flow | The movement of a liquid or gas. | | Viscosity | A measure of a fluid's resistance to flow; thicker fluids are more viscous. | | Laminar flow | A type of fluid flow where fluid particles move in smooth, parallel layers without crossing each other. | | Turbulent flow | A type of fluid flow characterized by irregular, chaotic motion with eddies and swirls. | | Equation of continuity | A principle stating that for an incompressible fluid flowing through a pipe, the flow rate is constant at all points, meaning the product of cross-sectional area and velocity is constant. | | Bernoulli’s principle | A principle stating that the pressure of a moving fluid decreases as its speed increases. | | Pascal’s law | A principle stating that a change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of the container. | | Archimedes’ principle | A principle stating that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. | | Buoyant force | The upward force exerted by a fluid on any immersed object. | | Density | The mass of a substance per unit volume. | | Pressure | Force exerted per unit area. | | Manometer | A device used to measure the pressure of a gas or liquid. | | Barometer | A device used to measure atmospheric pressure. | | Electromagnetic induction | The process by which a changing magnetic field induces an electromotive force (and thus a current) in a conductor. | | Magnetic flux | A measure of the total magnetic field lines passing through a given area. | | Transformer | An electrical device that transfers electrical energy from one circuit to another through electromagnetic induction, typically to change voltage levels. | | Semiconductor | A material with electrical conductivity between that of a conductor and an insulator. | | Doping | The process of adding impurities to a semiconductor material to alter its electrical conductivity. | | P-N junction | The interface formed when a P-type semiconductor is joined with an N-type semiconductor, forming the basis of diodes and transistors. | | Diode | A semiconductor device that allows current to flow in only one direction. | | Rectification | The process of converting alternating current (AC) into direct current (DC). | | Transistor | A semiconductor device with three terminals used to amplify or switch electronic signals. | | Integrated circuit (IC) | A small chip containing a complex electronic circuit made up of interconnected semiconductor devices. | | Logic gate | A fundamental building block of digital electronic circuits that performs a basic logical operation (e.g., AND, OR, NOT). | | Digital signal | A signal that represents data as a sequence of discrete values, typically high or low voltage levels. | | Analog signal | A continuous signal that represents information as a varying voltage or current. |