Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Electricity and Magnetism → Magnetism and Electromagnetism ↓


Faraday's and Lenz's laws


In the field of physics, particularly the study of electricity and magnetism, two important theories help us understand the interaction between magnetic fields and electric currents. These are Faraday's law of electromagnetic induction and Lenz's law. Both are the cornerstones of electromagnetism and have a wide variety of applications in the modern world, from the operation of electric generators to the functioning of transformers.

Faraday's law of electromagnetic induction

Michael Faraday discovered that changes in the magnetic field within a closed loop of wire can induce an electromotive force (EMF) in the wire. This phenomenon is described by Faraday's law, which is important for understanding how electric currents can be generated by magnetic fields. According to Faraday's law, the induced EMF in a circuit is directly proportional to the rate of change of the magnetic flux through the circuit.

EMF = -dΦ/dt

In this formula, EMF represents the induced electromotive force, dΦ represents the change in magnetic flux, and dt is the change in time.

Magnetic flux

Magnetic flux (Φ) is a measure of the number of magnetic field lines passing through a given area. It is calculated using the following formula:

Φ = B * A * cos(θ)

Where:

  • B is the magnetic field (T) in Tesla.
  • A is the area in square metres (m²) through which the field lines pass.
  • θ is the angle between the magnetic field lines and the perpendicular to the surface, expressed in degrees or radians.

To visualize magnetic flux, think of the magnetic field lines as the flow of a river. The magnetic flux then represents how much of this flux is passing through a net placed in the river. If the net is perpendicular to the flow (i.e., in the direct direction of the flow), the maximum flux passes through it. If the net is placed parallel to the river, fewer lines pass through, indicating less flux.

In the diagram above, the blue arrows represent magnetic field lines that cross a rectangular area perpendicular to them. Here the magnetic flux is at its maximum.

Understanding Lenz's law

Lenz's law works in conjunction with Faraday's law by determining the direction of induced emf and current as a result of changes in magnetic fields. It was formulated by Heinrich Lenz in 1834, stating that an induced current will appear in a closed conducting loop in the direction that opposes the change in magnetic flux that produces it.

The negative sign in the Faraday's Law equation EMF = -dΦ/dt represents Lenz's Law. This law is consistent with the law of conservation of energy, ensuring that the induced EMF produces a current that opposes the change in the magnetic field.

Illustration of Lenz's law

To better understand Lenz's law, take a simple example of a magnet and a coil:

  • If the north pole of a magnet is moving towards the coil, the magnetic field through the coil increases. According to Lenz's law, the induced current will flow in such a way that its own magnetic field will oppose this increase. This means that the coil will have its north pole facing the north pole of the magnet, which will repel the approaching magnet.
  • Conversely, if the north pole of the magnet is moving away from the coil, the magnetic field through the coil decreases. The induced current will produce a magnetic field in such a direction to oppose this decrease. This time, the coil will produce a south pole facing the repelling north pole of the magnet, effectively attracting it.
N

With this diagram, see how the magnetic field lines from a north pole magnet interact with the coil. If the magnet coil moves or the magnets themselves move (either toward or away from each other), the direction of the current changes according to Lenz's law, which opposes this motion.

Applications of Faraday's and Lenz's laws

Both laws play an integral role in modern technology. Let's examine some of the major applications:

Electric generator

An electric generator converts mechanical energy into electrical energy by rotating a coil in a magnetic field. As the coil rotates, the magnetic flux changes with time, inducing an EMF (as described by Faraday's law). The direction of the induced current, which is consistent with Lenz's law, ensures that energy is not created or lost, but only transformed.

Transformers

Transformers play a vital role in power transmission. They work on the principles of Faraday's law. When an alternating current passes through the primary coil, it produces a change in the magnetic field, which induces a voltage in the secondary coil. The direction and magnitude of this induced voltage follow Lenz's law and are controlled to ensure efficient energy transfer.

Eddy currents

When a conductor passes through a magnetic field or when the magnetic field around a stationary conductor changes, eddy currents are induced within the conductor. These currents create magnetic fields which oppose the change according to Lenz's law. Eddy currents are used in induction heating and braking systems in trains.

Conclusion

Faraday's and Lenz's laws are fundamental principles of electromagnetism that explain how electric currents can be generated from changing magnetic fields. Through these laws, we understand the fundamental interactions between electric and magnetic fields, the explanation of which illuminates many natural phenomena and provides solutions to technical problems in engineering and everyday life. Their applications span a variety of devices and technologies that form the backbone of modern civilization, continuing to influence advances in the way we harness and use energy.


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Faraday's and Lenz's laws

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