. Physics SS 3 \u00a0 Theme 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Conservation Principles\u00a0 Energy and Society Conversion of Energy Theme 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Waves, Motion without Material Transfer\u00a0\u00a0\u00a0 Properties of Waves Electromagnetic Waves Theme 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Fields at Rest and In Motion\u00a0\u00a0\u00a0\u00a0\u00a0 Gravitational Field Electric Field Magnetic fields Electro-magnetic Field Simple A.C. circuits Theme 4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Energy Quantization and Duality of Matter\u00a0\u00a0\u00a0\u00a0\u00a0 Models of the atom Nucleus Energy quantization Duality of Matter Theme 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Physics in Technology\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Battery Electroplating Application of Electromagnetic field Transmission systems Uses of machines Repairs and maintenance of machines Dams and Energy Production Rockets and Satellites Niger-SAT I NICOM-SAT I \u00a0 \u00a0 Theme 1\u00a0 Conservation Principles Energy and Society The sources of energy: Energy sources are the various forms of natural resources that can be converted into usable energy for various purposes. These sources can be categorized into two main types: primary and secondary. Primary sources include fossil fuels (coal, oil, natural gas), renewable sources (solar, wind, hydro, geothermal), and nuclear fuels. Secondary sources are derived from primary sources and include electricity and hydrogen. \u00a0 Distinguish between renewable and non-renewable sources of energy: Renewable sources of energy are those that can be naturally replenished over a relatively short period of time. Examples include solar energy (from sunlight), wind energy, hydroelectric energy (from flowing water), and geothermal energy (from Earth's heat). Non-renewable sources, on the other hand, are finite and deplete over time as they are used. These include fossil fuels (coal, oil, natural gas) and nuclear fuels. The key distinction is that renewable sources are sustainable in the long term, while non-renewable sources are not. \u00a0 The uses and importance of energy in the development of society: Energy is essential for the development of society as it powers various aspects of modern life. It is used for electricity generation, transportation, heating, cooling, industrial processes, and more. Reliable and affordable energy access is a cornerstone of economic growth, technological advancement, and improved living standards. Without energy, many of the conveniences and technologies we rely on today would not be possible. \u00a0 Impact\/effects of energy usage on the environment: Energy usage, particularly from non-renewable sources, has significant environmental impacts. Burning fossil fuels releases greenhouse gases (such as carbon dioxide) into the atmosphere, contributing to climate change and global warming. Extracting and processing these fuels can lead to habitat destruction, air and water pollution, and oil spills. Nuclear energy, while low in carbon emissions, poses risks in terms of radioactive waste disposal and potential accidents. These environmental impacts highlight the importance of transitioning to cleaner and more sustainable energy sources. \u00a0 Energy sources that are environmentally friendly and those that are hazardous to the environment: Renewable energy sources like solar, wind, hydro, and geothermal are generally considered environmentally friendly because they produce little to no greenhouse gas emissions during operation. They have minimal negative impacts on air and water quality. Fossil fuels and nuclear energy, on the other hand, are more hazardous to the environment due to their emissions, waste products, and potential for accidents. \u00a0 Conservation of energy: Conservation of energy refers to the practice of using energy resources more efficiently and responsibly to reduce waste and environmental impact. This involves adopting energy-saving technologies, improving energy efficiency in buildings and transportation, and promoting sustainable practices. Conservation helps extend the availability of finite resources, reduces pollution, and mitigates the impacts of energy consumption on the environment. It's a crucial component of a sustainable energy future. \u00a0 Remember that these explanations provide a broad overview of each topic. There are many complexities and nuances within each area, but I hope this helps you understand the basics of energy sources, their impact on society and the environment, and the importance of conservation. \u00a0 \u00a0 Conversion of Energy DEFINITION OF ENERGY CONVERSION Energy conversion, also referred to as energy transformation, entails the process of altering energy from one form to another. \u00a0 VARIETIES OF ENERGY CONVERSION Transformation of mechanical energy results in heat energy. Conversion of electrical energy leads to mechanical energy, as seen in devices like blenders and electric cookers. Electricity can be converted into heat energy, as demonstrated by appliances like clothes irons and electric stoves. Mechanical energy can be transmuted into electrical energy. Chemical energy can be changed into heat energy, exemplified by the usage of kerosene stoves. Solar energy can be metamorphosed into heat energy, chemical energy, and electrical energy. Light energy can be modified into heat energy. \u00a0 SIGNIFICANCE OF ENERGY CONVERSION Economic savings are realized. Pollution is diminished. Energy is conserved. Energy generation occurs. Renewable energy sources replace nonrenewable ones. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Theme 2\u00a0 Waves, Motion without Material Transfer Properties of Waves A wave is a phenomenon characterized by the transfer of energy through a medium without the physical movement of the medium itself over a long distance. Waves can take various forms, including mechanical waves, which require a medium (like air, water, or solid material) to travel through, and electromagnetic waves, which can propagate through a vacuum (such as light or radio waves). \u00a0 Mechanical waves can be further categorized into two main types: Transverse Waves: In transverse waves, the particles of the medium move perpendicular to the direction in which the wave is travelling. An example of a transverse wave is a wave on a string. Longitudinal Waves: In longitudinal waves, the particles of the medium move parallel to the direction of the wave propagation. An example of a longitudinal wave is a sound wave in air. \u00a0 Electromagnetic waves, on the other hand, consist of oscillating electric and magnetic fields that can travel through a vacuum. These waves include various forms of light, such as radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. \u00a0 Waves are described by various properties, including: Amplitude: The maximum displacement of a particle from its equilibrium position in a wave. Wavelength: The distance between two consecutive points that are in phase (for example, two peaks or troughs) in a wave. Frequency: The number of complete oscillations (cycles) of a wave that occur in a unit of time. It is measured in Hertz (Hz). Period: The time it takes for one complete oscillation of a wave to pass a given point. Velocity: The speed at which a wave propagates through a medium, which is related to its frequency and wavelength. \u00a0 Waves play a crucial role in various natural phenomena and technological applications. They are essential for communication (radio, TV, and cellular signals), medical imaging (X-rays and ultrasound), and understanding the behaviour of particles at the atomic and subatomic scales. \u00a0 Wave Properties The attributes of waves manifest in diverse ways, conveniently demonstrated through the use of a ripple tank. The apparatus comprises a transparent container filled with water, beneath which lies a white screen. Positioned above is a light source, while a small electric motor (vibrator) is attached to induce disturbances that give rise to waves. The movement of wavefronts delineates the patterns of these waves during their propagation. \u00a0 Straight-line Propagation (Rectilinear Propagation) One of the inherent traits of waves involves their travel in unswerving trajectories, perpendicular to their wavefronts. The ensuing illustrations portray the direct course of water waves as they advance. \u00a0 Wave Bending (Refraction) Refraction is the phenomenon where waves alter their trajectory upon crossing a boundary between different mediums. This transformation arises when waves encounter an obstacle obstructing their path. Notably, this directional shift materializes specifically at the juncture between deep and shallow waters, and solely when waves strike the boundary at an angle. \u00a0 Wave Diffraction When waves traverse the edge of an obstacle or a narrow aperture, they incline to curve around the corner and disperse beyond the hindrance or opening. \u00a0 Wave Interference Wave interference unfolds when two waves conflate, yielding outcomes that can range from significantly amplified waves to diminished ones, or even the absence of waves entirely. In-phase waves combine constructively, intensifying their effects. Conversely, out-of-phase waves nullify each other, leading to destructive interference. \u00a0 Sound Interference In an illustration of sound interference, two loudspeakers, L1 and L2, are linked to a common signal generator, aligning the phases of their emitted sound waves. Positioned roughly half a wavelength apart (around 0.5 meters for a sound frequency of 1,000 Hz), the speakers exhibit alternating increments and decrements in sound intensity along line AB. This occurrence demonstrates both constructive and destructive interference. \u00a0 Formation of Stationary Waves Stationary waves, also recognized as standing waves, manifest when two identical progressive waves moving in opposing directions superimpose. Placing two opposing speakers face to face or securing one end of a rope produces these stationary wave patterns. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Electromagnetic Waves 1. Differences between Electromagnetic Waves and Mechanical Waves: Electromagnetic Waves: These are waves that consist of oscillating electric and magnetic fields. They do not require a medium (substance) to travel through and can propagate through vacuum (empty space). Examples include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. \u00a0 Mechanical Waves: These waves require a medium to travel through, such as a solid, liquid, or gas. They involve the physical displacement of particles in the medium as the wave passes through. Examples include sound waves, water waves, and seismic waves. The key distinction is that electromagnetic waves can travel through vacuum, while mechanical waves require a physical medium for propagation. \u00a0 Uses of Electromagnetic Waves and Their Sources: Uses of Electromagnetic Waves: Radio Waves: Used for radio and television broadcasting. Microwaves: Used in microwave ovens for cooking, as well as for wireless communication. Infrared Radiation: Used in remote controls, thermal imaging, and some medical applications. Visible Light: Used for human vision, photography, and illumination. Ultraviolet Radiation: Used in sterilization, security marking, and tanning beds. X-rays: Used in medical imaging (X-ray radiography and CT scans) and materials testing. Gamma Rays: Used in medical imaging and cancer treatment. \u00a0 Sources of Electromagnetic Waves: Radio Waves: Generated by electronic circuits in radio and TV broadcasting stations. Microwaves: Produced by microwave generators in appliances like microwave ovens and communication devices. Infrared, Visible Light, Ultraviolet: Emitted by heated objects, incandescent bulbs, lasers, and electronic transitions in atoms. X-rays: Produced by X-ray machines where high-speed electrons collide with a metal target. Gamma Rays: Emitted by radioactive decay and nuclear reactions. \u00a0 Comparing and Contrasting Frequency and Wavelength: Frequency: Definition: Frequency refers to the number of oscillations or cycles of a wave that occur in a unit of time (usually per second, measured in Hertz, Hz). Symbol: Represented by the symbol "f." Relation to Energy: Higher frequency corresponds to higher energy for electromagnetic waves (e.g., gamma rays have high frequency and energy). Relation to Pitch: In sound waves, higher frequency corresponds to higher pitch. \u00a0 Wavelength: Definition: Wavelength is the distance between two consecutive points in a wave that are in phase (e.g., between two crests or two troughs). Symbol: Represented by the symbol "\u03bb" (lambda). Relation to Energy: Inversely related to frequency for electromagnetic waves \u2013 higher frequency corresponds to shorter wavelength and higher energy. Relation to Sound: In sound waves, shorter wavelength corresponds to higher frequency and higher pitch. \u00a0 Comparison: Frequency and Wavelength Relationship: They are inversely proportional for electromagnetic waves \u2013 as frequency increases, wavelength decreases, and vice versa. Propagation Speed: Higher frequency does not necessarily mean a higher propagation speed; it depends on the medium. In a vacuum, all electromagnetic waves travel at the speed of light. Applicability: Frequency is often used when discussing the properties and applications of electromagnetic waves, while wavelength is important for understanding diffraction, interference, and other wave behaviours. \u00a0 Electromagnetic waves and mechanical waves have distinct characteristics, uses, and sources. Frequency and wavelength are essential properties of waves that are interconnected and play roles in determining wave behavior and applications. \u00a0 DEFINITION AND CONCEPT Electromagnetic waves are produced by electromagnetic vibrations. Electromagnetic waves have an electrical origin and the ability to travel in a vacuum.\u00a0 So, electromagnetic waves are regarded as a combination of travelling electric and magnetic forces which vary in value and are directed at right angles to each other and to the direction of travel.\u00a0 In other words, they are transverse waves. TYPES OF RADIATION The electromagnetic waves consist of the following: Radio waves with wavelength 10 raise to minus 3 meters to 1000 meters. Infra-red waves with average wavelengths of 10 raise to power minus 6 meters. Visible spectrum, known as light waves, with wavelengths of 7 times 10 raise to the power of minus 7 meters for red rays. Ultraviolet rays with a wavelength of 10 raise to the power of minus 8 meters X-rays with a wavelength of 10 raise to the power of minus 10 meters. Gamma\u2013rays with a wavelength of 10 raise to the power of minus 11 meters. \u00a0 Radio waves: Radio waves have the longest wavelengths.\u00a0 Radio waves are emitted from transmitters and carry radio signals to radio sets.\u00a0 The shortest radio waves are called microwaves.\u00a0 Microwaves are used in radar and in heating hence they are used in cooking Infra-red waves: Infra-red waves are found just beyond the red end of the visible spectrum. They are present in the radiation from the sun or from the filament of an electric lamp. Many manufacturing industries used infra-red lamps to dry paints on painted items. They are also used for the treatment of muscular Visible Spectrum or Light Waves: The visible spectrum is made up of red, orange, yellow, green, blue, indigo and violet rays. These are all colours of the rainbow. When these rays combine, they form a white light.\u00a0 In the visible spectrum, red rays have the longest wavelengths while the violet rays have the shortest wavelengths. The main source of light is the sun Ultra Violet Rays: Ultra violet rays are located just beyond the violet end of the visible spectrum. Ultraviolet rays can be produced by quarts, mercury filaments, or the sun. Ultraviolet rays can cause certain materials to fluoresce (that is. glow) X-Rays: rays are produced when fast moving electrons strike a metal target, which reduces their velocity. X- Rays are used in hospitals to destroy malignment growth in the body and to produce x-ray photographs which can locate broken bones. Much of x- ray in the body is harmful and can lead to sterility and adverse change in the blood. X-rays are used in industry to locate cracks in metal castings and flows in pipes. X-rays ionize gases and have a penetrating effect such that they pass through substances opaque to white light are diffracted by crystals and are unaffected by either electric or magnetic fields. Gamma \u2013 Rays: Gamma rays are emitted by radioactive substances such as cobalt. 60. Like x-rays, gamma rays ionize gases and darken photographic plates. Because of their shorter wavelengths, gamma rays have a greater penetrating power. \u00a0 DETECTORS The detectors of the various radiations in the electromagnetic spectrum are Gamma rays - Geiger-Muller tube X- rays - Photographic films Ultraviolet rays - Photographic films, fluorescent substances Visible rays - Eye, photographic film, photo electric cell Infra-red rays - Skin, thermometer, photo transistor, photographic film. Radio waves - Radio set, Television set, Aerials \u00a0 USES Radio waves are very important for effective communication especially when radio sets, television sets, and walkie-talkie are involved. Knowledge of infrared rays is used in developing infra-red telescopes, and infra-red signalling lamps which are useful to soldiers fighting in darkness. With the aid of photographic film which is sensitive to infra-red, it is possible to take clear photographs through mist and haze. X-rays are useful in hospitals (e.g. to inspect broken bones), industry (to inspect metal castings), and in science to study the crystal structure of matter. Gamma rays are used to kill cancer cells in patient\u2019s body as well as bacteria in foods and hospital equipment. Knowledge of ultraviolet rays is used in developing ultraviolet lamps; the lamps are useful in conducting experiments on the photo-electric effect. \u00a0 \u00a0 \u00a0 Theme 3\u00a0 Fields at Rest and In Motion Gravitational Field Newton's Law of Universal Gravitation: This law states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In mathematical terms, it can be expressed as: \u00a0\u00a0 F = G x M1 M2\/r2 where F is the gravitational force between two masses m1 and m2, r is the distance between their centres, and G is the gravitational constant. \u00a0 Calculating Gravitational Force: To calculate the gravitational force between two masses (or planets), you can use the formula mentioned above. Plug in the values of the masses and the distance between them to find the force. Keep in mind that the units of mass should be in kilograms, the distance in meters, and the gravitational constant G is approximately 6.67430 x 10-11m3kg-1 s-2. \u00a0 Kepler's Laws of Planetary Motion: Johannes Kepler formulated three laws that describe the motion of planets in the solar system: First Law (Law of Orbits): Each planet orbits the Sun in an elliptical path, with the Sun at one of the two foci. Second Law (Law of Areas): A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means a planet moves faster when it is closer to the Sun (perihelion) and slower when it is farther (aphelion). Third Law (Law of Harmonies): The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Mathematically: T2 \u221d a3, where T is the orbital period and a is the semi-major axis. \u00a0 Natural vs. Artificial Satellites: Natural Satellites: These are celestial bodies that orbit larger celestial bodies naturally. For example, the Moon is a natural satellite of Earth. Artificial Satellites: These are human-made objects intentionally placed into orbit around Earth or other celestial bodies. Examples include communication satellites, weather satellites, and research satellites. \u00a0 Satellite Launch: Satellites are launched into space using rockets. The satellite is placed in a payload compartment atop the rocket. The rocket carries the satellite into space and releases it into the desired orbit. Once in orbit, the satellite's onboard propulsion system can fine-tune its position. \u00a0 Uses of Satellites: Satellites have a wide range of applications, including but not limited to: Communication: Satellites enable global communication through television, internet, and telephone services. Earth Observation: Satellites monitor weather, climate, natural disasters, and land use. Navigation: Satellite-based navigation systems like GPS provide accurate positioning and timing information. Scientific Research: Satellites are used to study space phenomena, cosmic radiation, and other astronomical observations. Military and Defense: Satellites aid in reconnaissance, surveillance, and intelligence gathering. \u00a0 Escape Velocity and Inverse Square Law: The escape velocity is the minimum velocity an object needs to break free from a celestial body's gravitational field and move into space. It can be calculated using the formula: \u00a0\u00a0 Vesc = \u222b2.G.M\/r\u00a0 where M is the mass of the celestial body (e.g., Earth), r is the distance from the object to the centre of the celestial body, and G is the gravitational constant. The escape velocity is derived using the principles of potential and kinetic energy and is based on the inverse square law, which relates the intensity of a force to the square of the distance from the source of that force. \u00a0 \u00a0 Electric Field Converting Galvanometer to Ammeter and Voltmeter: A galvanometer is an instrument used to detect small electric currents. To convert a galvanometer into an ammeter (a device that measures current) or a voltmeter (a device that measures voltage), a shunt resistor or a series resistor is added, respectively. \u00a0 Ammeter: To convert a galvanometer into an ammeter, a low-resistance shunt resistor is connected in parallel with the galvanometer. This shunt resistor diverts most of the current, allowing only a known fraction to pass through the galvanometer. The value of the shunt resistor is calculated based on the desired full-scale deflection of the ammeter. \u00a0 Voltmeter: To convert a galvanometer into a voltmeter, a high-resistance series resistor is connected in series with the galvanometer. This series resistor limits the current passing through the galvanometer, ensuring that it is only exposed to a small fraction of the total voltage across the circuit. The value of the series resistor is determined by the desired voltage range of the voltmeter. \u00a0 2. Principle of Potentiometer: The potentiometer is a device used to measure the electromotive force (emf) or potential difference between two points in an electrical circuit. It operates on the principle of the potential gradient along a uniform wire. When a constant current flows through the wire, the potential difference across any segment of the wire is directly proportional to its length. By adjusting a sliding contact along the wire, the point where the potential matches the unknown potential can be determined. This provides a means to measure unknown voltages by comparing them to a known voltage. \u00a0 Electric Field Intensity vs. Electric Potential: Electric Field Intensity: Electric field intensity, represented by 'E', is a vector quantity that describes the force experienced by a positive test charge placed in an electric field. It's the force per unit of positive charge at a point in space. The unit of electric field intensity is volts per meter (V\/m). \u00a0 Electric Potential: Electric potential, often referred to as voltage, is a scalar quantity that represents the amount of work needed to move a positive test charge from a reference point to a specific point in an electric field, divided by the charge's magnitude. It's measured in volts (V). \u00a0 Solving Problems on Electric Field Intensity and Electric Potential: \u00a0\u00a0 - To solve problems related to electric field intensity and electric potential, you typically apply the principles of Coulomb's law and the formulas derived from it. Coulomb's law gives the electric field due to a point charge, while the electric potential due to a point charge is calculated using the formula V = kQ\/r, where k is the electrostatic constant, Q is the charge, and r is the distance. \u00a0 Coulomb's Law and Related Questions: Coulomb's Law: Coulomb's law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, F = k * |q1 * q2| \/ r^2, where F is the force, q1 and q2 are the charges, r is the distance between them, and k is the electrostatic constant. \u00a0 Solving Questions: To solve problems related to Coulomb's law, you apply the formula mentioned above. You can calculate the force between charges, the magnitude of charges given a force, or distances given force and charges. \u00a0 Remember to use consistent units and pay attention to the signs of charges to ensure accurate calculations. CAPACITORS AND CAPACITANCE \u00a0\u00a0However, most common types of capacitors are in the form of two parallel plate conductors which are separated by a very small distance, d. The two plates of the capacitor can be made to carry equal and opposite charges by connecting the capacitor across the terminals of a battery such that the potential difference across the plate is V. Capacitor is represented as\u00a0 \u00a0 CAPACITANCE The capacitance of a capacitor is defined as the ratio of the charge Q on either conductor to the potential difference V between the two conductors C = Q over V Q = CV The SI unit of capacitance is the farad (F) which is equivalent to coulomb per volts (CV-1) Factors that affect the capacitance of a capacitor are: The area of the plates The separation between the plates The di-electric substance between the plates For a parallel plate capacitor, the capacitance C is given by C = A over d Where: A= area of the plates d= their separation \u025b= permittivity of the dielectric medium (Fm-1) CAPACITOR IN SERIES AND IN PARALLEL If two or more capacitors is c1, c2 \u2026 are connected in series, it can be shown that the equivalent or net capacitance, c of the combination is given by: 1\/c = 1 over c1 + 1over c2 +\u2026 If they are connected in parallel the net capacitance C in this is given by: C = c1 + c2 + \u2026 Note that the opposite is the case if these were resistance. \u00a0 SIMPLE PROBLEMS A capacitor contains a charge of 4 .0 x 10 raise to power minus 4 coulomb when a potential difference of 400 v is applied across it. Calculate the capacitance of the capacitor The capacitance C = q divided by v = 4.0 times 10 raise to the power of minus 4, then divided by 400 = 10 raise to the power of minus 6 F = 1.0f ENERGY STORED IN THE CAPACITOR A charge is a store of electrical energy. When a charge, q , is moved through a p.d , the work done is given by \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 W = average p.d times charge \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = half of qv = half of QV \u00a0\u00a0\u00a0\u00a0\u00a0 But v = Q over C; V = Q, divided by C W = half of Q \/ C times q =half of q square\/c W = half of Q\/C Using Q = CV W =1\/2CV raise to the power of 2 Therefore, the work done is either \u00bc1 over 4 times q square divided by C or half of cv raise to power 2, which is W = half of CV raise to power 2. This work is stored in the capacitor as electrical potential energy Magnetic fields MAGNET AND ITS PROPERTIES A magnet is any material that is capable of attracting other pieces of the same material as well as pieces of iron. A substance is said to be ferromagnetic if it is attracted by a magnet. Examples are iron, cobalt, Nickel, and certain alloys. Substances which cannot be attracted by a magnet are called non-magnetic material e.g. brass, wood, copper, and glass. Properties of magnets The ends of a magnet where the attracting power is greatest are called the poles. A bar magnet suspended freely in a vertical plane called magnetic meridian comes to rest with its axis in the North-South direction. The part which points northwards is called the north seeking pole or North Pole while the opposite pole is called the South Pole Like poles of magnet repel each other while unlike poles attract each other. The polarity of a magnet can be tested by bringing both poles in turn nearer to the known pole of a suspended magnet. Repulsion indicates similar polarity. Attraction could be due to two unlike poles or a pole and a piece of un-magnetized material. Hence, repulsion is the only sure test for polarity. \u00a0 MAGNETIZATION AND DEMAGNETIZATION Magnetization is a process whereby a material is made to become magnetic. This can be achieved through any of the following methods: Electrical method - A cylindrical coil wound with several turns of insulated copper wire is connected in series with a six or twelve volt electric battery and switch. A coil of this type is called a solenoid. A steel bar is placed inside the coil and the current is switched on for some time. On removing and testing the steel, it will be found to have been magnetized. It is unnecessary to leave the current for long as length of time makes no difference but causes over-heating. The induced polarity depends on the direction of flow of the current. Clockwise flow at an end indicates South Pole while an anti-clockwise flow indicates North Pole. Single touch method - A steel bar is stroke from end to end several times in the same direction with a known pole of a magnet. Between successive strokes the pole is lifted high above the bar otherwise the magnetism already induced will be weakened. The disadvantage of this method is that it produces magnets in which one pole is nearer the end of the bar than the other. Divided touch method - Here the steel bar is stroked from the centre outward with unlike poles of two magnets simultaneously. The polarity produced at the end of the bar where the stroking finishes is of the opposite kind to that of the stroking pole. Hammering in the earth field - Magnets can be made by hammering a red hot steel bar and allowing it to cool as it lies in a North-South direction. Induced Magnetism - When a piece of un-magnetized steel is placed either near or in contact with a pole of a magnet and then removed, it will be magnetized. This is called induced magnetism. The induced pole is of the opposite sign to that of the inducing pole. \u00a0 DEMAGNETIZATION This is a process whereby a magnet is made to lose its magnetism. Demagnetization can be achieved by: Electrical Method - The magnet is placed in a solenoid through which an alternating current is flowing. The solenoid is placed with its axis pointing in the East-West direction. After a few seconds, the magnet is slowly withdrawn out of the solenoid to a long distance away. This is the most efficient way of demagnetizing a magnet. Mechanical Method - Another method of demagnetizing magnets is to hammer it hard when it is pointing in the East-West direction. Heating Method - When magnets are strongly heated, it lose their magnetism. TEMPORARY AND PERMANENT MAGNET Soft iron is pure iron while steel is an alloy of iron and carbon. Steel is a much harder and stronger material than soft iron. Steel and iron have different magnetic properties. Iron is easily magnetized than steel but it readily loses its magnetism. Steel produces a stronger magnet which is the reason why steel is used for making permanent magnet such as compass needle. In temporary magnets where the magnetism is required for a short MAGNETIC FIELDS Magnetic field is the space surrounding the magnets in which magnetic force is exerted. It is a vector quantity and it is represented by magnetic lines. The direction of the magnetic flux at any point is the direction of the force on a north pole placed at that point. In the neighbourhood of two magnets placed closed together, there exists a field in which the direction of the magnetic flux changes rapidly in a confined space. The magnetic flux can be obtained by using iron fillings. A magnetic meridian at any place is a vertical plane containing the magnetic axis of a freely suspended magnet at rest under the action of the earth field. The geographical meridian at a place is a plane containing the place and the earth's axis of rotation. The angle between the magnetic and geographical meridian is called the magnetic declination. The angle of dip or inclination is the angle between the direction of the earth magnetic flux and the horizontal. \u00a0 Relationship between Magnetic Force and Motion of a Charge in a Magnetic Field: When a charged particle, such as an electron or a proton, moves through a magnetic field, it experiences a force known as the magnetic force. This force is perpendicular to both the velocity of the charged particle and the direction of the magnetic field. The relationship between the magnetic force and the motion of the charge can be described by the Lorentz force equation: F = Q x V x B Where: F is the magnetic force experienced by the charge. Q is the charge of the particle. V is the velocity of the particle. B is the magnetic field vector. \u00a0 This equation tells us that the magnetic force is directly proportional to the charge of the particle, the magnitude of its velocity, the strength of the magnetic field, and the sine of the angle between the velocity and the magnetic field direction. The magnetic force doesn't do any work on the charged particle; it only affects its direction, causing it to move in a circular or helical path, depending on the initial velocity and the orientation of the magnetic field. \u00a0 Terms Used in Magnetism: (a) Angle of Declination: The angle of declination, also known as the magnetic declination or magnetic variation, is the angle between the direction of the true geographic north (geographic meridian) and the direction of the north pole of a magnetic compass needle. In other words, it represents the difference between true north (geographic north) and magnetic north. This angle varies based on your location on Earth and changes over time due to the movement of Earth's magnetic poles. \u00a0 (b) Angle of Dip: The angle of dip, also known as the magnetic inclination, is the angle between the direction of a magnetic needle that moves freely in the vertical plane and the horizontal plane of the Earth. It indicates how much the magnetic field lines are inclined from the horizontal at a specific location. At the magnetic equator, the angle of dip is 0 degrees (parallel to the Earth's surface), while at the magnetic poles, it's 90 degrees (pointing directly downward). \u00a0 (c) Neutral Point: In the context of Earth's magnetic field, a neutral point is a location where the horizontal component of the Earth's magnetic field is so strong that it neutralizes the vertical component. At this point, a magnetic needle will not show any inclination (angle of dip), as it will align parallel to the Earth's surface. Neutral points are important when considering the behaviour of magnetic compass needles and their inclination in various locations. These terms are essential in understanding the behavior of magnetic fields, compasses, and how Earth's magnetic properties vary across different locations. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Electro-magnetic Field PATTERNS OF MAGNETIC FIELDS Magnetic field patterns can easily be observed using iron fillings.\u00a0 The magnetic is put on paper and the iron fillings are sprinkled lightly on the paper around the magnet.\u00a0 The paper is tapped gently and the iron fillings are found to turn and set to in a definite direction. MAGNETIC FIELD AROUND A STRAIGHT CONDUCTOR CARRYING CURRENT \u00a0A straight conductor carrying current can be shown that it has a magnet filed around it.\u00a0 Allow a thick isolated copper wire to pass vertically through a hole in a cardboard shit.\u00a0 As shown below, sprinkle some iron fillings uniformly on the cardboard around the vertical wire connect the ends of the wire to a battery, switch on the current and place some compass needles around the wire.\u00a0 Note the direction to which the compass needle point.\u00a0 Switch on the current and note the swing of the needles and how they point. It will be observed that when current is switch on and the card board is gently tapped, the fillings arrange themselves in a series of concentric circles about the wire as centre. Also as soon as the current is switch on, the needles will swing around and form a circle with the wire as centre.\u00a0 The direction of the filed depends on the direction of flow of the current.\u00a0 Such a direction can always be obtained by applying the Right Hand Grip Rule. \u00a0 \u00a0 \u00a0 FORCE ON A CURRENT CARRYING CONDUCTOR IN A MAGNETIC FIELD A conductor carrying an electric current, when placed in the magnetic field experiences a mechanical force. This can be demonstrated by using two metal rails fixed on each side of a powerful horse-shoe magnet. A copper rod is placed across the rays. When the current is passed through this copper rod, it is observed that the copper rod rolls along the rays, toward the right. If by adjusting the rheostat, more current is made to flow through the rod. One will notice that the rod moves faster, thus the force on the rod increases when the current increases.\u00a0 If the direction of flow of current is reversed by reversing the connections at the battery terminals, the rod will be observed to move towards the left, opposite to the previous direction of motion. If one turns the magnet such that the magnetic field is parallel to the length of the rod as shown below, it will be observed that the current carrying the rod remains stationary no matter the amount of current hat pass through.\u00a0 There is therefore no force on the rod. ELECTROMAGNETIC FIELD: This is a field representing the joint interaction of electric and magnetic forces.\u00a0 It is exerted on charged particles.\u00a0 The force on a charge q moving with velocity v less than the velocity of light is given by \u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 F = q (E + v x B) A conductor carrying an electric current when placed in a magnetic field experiences a mechanical force. It can be demonstrated by using two metal rails fixed on each side of a powerful horseshoe magnet.\u00a0 A copper rod is placed across the rails.\u00a0\u00a0 When we pass current through this copper rod, it is observed that the copper rod rolls along the rails, towards the right.\u00a0 If by adjusting the rheostat, we cause more current to flow through the rod, we will observe that the rod moves faster. Thus, the force on the rod increases when the current increases. Direction of the force The direction of force on a current carrying conductor placed perpendicular to the magnetic field is given by Fleming\u2019s left-hand rule which is stated as follows: If the thumb, forefinger and middle finger are held mutually at right angles to one another with the fore-finger pointing in the direction of magnetic field, and the second finger in the direction of Current, then the thumb will point in the direction of the force producing motion. APPLICATIONS OF ELECTROMAGNETIC FIELD Electric Motor - The electric motor is a device for converting electrical energy into chemical energy. It consists: \u00a0(a) A rectangular coil of insulated wire, known as armature \u00a0(b) A powerful magnetic field in which the armature turns is provided by two curve pole pieces of a powerful magnet (c) A commutator consisting of a split copper ring, two halves of which are insulated from each other.\u00a0\u00a0 (d). Two carbon brushes which are made to press lightly against either side of the split-ring commutator Moving Coil Galvanometer - This galvanometer is one of the most sensitive and accurate methods for detecting or measuring extremely small currents or potential differences. It consists essentially of A light rectangular vertical coil ABCD pivoted in jewelled bearings such that it can move in a vertical plane b. Two curved pole pieces of a horseshoe magnet and a soft iron core or cylinder are inserted between the pole pieces. Two spiral non-magnetic control springs of phosphor bronze, each of which is attached to the jeweled bearing or spindle. Current enters or leaves the rectangular coil through these spiral springs.\u00a0 The springs also provide the control couple. \u00a0 Electromagnetic Induction and Fleming's Rules: Electromagnetic Induction: This is the process of generating an electromotive force (EMF) or voltage in a circuit by changing the magnetic field through the circuit. This phenomenon was discovered by Michael Faraday in the early 19th century. Electromagnetic induction is based on the principle that a change in magnetic field flux through a closed circuit induces a voltage and, consequently, an electric current in that circuit. \u00a0 Fleming's Rules: these are a set of three rules that describe the direction of induced current and the motion of a conductor in relation to the magnetic field. These rules were formulated by John Ambrose Fleming and help determine the direction of the induced current or the motion of the conductor in electromagnetic induction situations. \u00a0 Faraday's Laws of Electromagnetic Induction: Faraday's First Law: This law states that when there is a change in magnetic flux through a closed circuit, an electromotive force (EMF) is induced in the circuit. The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux. \u00a0 Faraday's Second Law: This law states that the induced EMF in a closed circuit is equal to the negative rate of change of magnetic flux. Mathematically, this can be represented as: EMF = -d(\u03a6) \/ dt, where EMF is the induced electromotive force, \u03a6 is the magnetic flux, and dt is the change in time. \u00a0 Conversion Principle Involved: Both of Faraday's laws are based on the conversion of mechanical energy (motion or change in magnetic field) into electrical energy (induced EMF and current). The change in the magnetic field or motion of a conductor induces an electric current by exploiting the relationship between magnetic fields and electric fields. \u00a0 Use of Induction Coils and Transformers: Induction Coils: Induction coils are devices that use electromagnetic induction to amplify low-voltage signals to higher voltages. They consist of two coils, a primary and a secondary, wound around a common iron core. When the current in the primary coil changes, it induces a changing magnetic field, which in turn induces a voltage in the secondary coil. \u00a0 Transformers: Transformers are devices that utilize electromagnetic induction to change the voltage level of alternating current (AC) while maintaining power efficiency. They consist of primary and secondary coils wound around a shared iron core. Transformers can step up (increase voltage) or step down (decrease voltage) AC voltages. Lamination of Transformer and Induction Cores: The cores of transformers and induction coils are laminated to reduce energy losses due to eddy currents. Eddy currents are small circular currents that can form within the core material when it's exposed to a changing magnetic field. These currents generate heat and waste energy. Laminating the core with thin sheets of a material like silicon steel reduces the formation of eddy currents and thus improves the efficiency of the device. \u00a0 AC and DC Generators: AC Generators (Alternators): AC generators, also known as alternators, are devices that convert mechanical energy into alternating current (AC) electrical energy. They work on the principle of electromagnetic induction. The generator consists of a rotating coil within a magnetic field. As the coil spins, the magnetic field through the coil changes, inducing an alternating voltage. \u00a0 DC Generators: DC generators, also known as dynamos, convert mechanical energy into direct current (DC) electrical energy. They also operate based on electromagnetic induction. The key difference is in the commutator and brush arrangement. A commutator in a DC generator reverses the direction of the current every half rotation, resulting in a unidirectional current flow. \u00a0 Electromagnetic induction is the process of generating an EMF in a circuit due to changes in magnetic field flux. Fleming's rules help determine the direction of induced current. Faraday's laws describe the quantitative relationship between induced EMF and magnetic flux changes. These principles are applied in various devices like induction coils and transformers, with laminated cores to minimize energy losses. AC and DC generators both utilize electromagnetic induction, but they differ in their current output and mechanism of generating a unidirectional current.