NCERT · Class 12 · Physics · Electromagnetic InductionState Faraday's laws of electromagnetic induction. Express Lenz's law and explain briefly how Lenz's law is in accordance with the law of conservation of energy.

Faraday's Laws of Electromagnetic Induction:

1. First Law: Whenever the magnetic flux linked with a closed circuit changes, an electromotive force (emf) is induced in the circuit. The induced emf lasts as long as the change in magnetic flux continues.
2. Second Law: The magnitude of the induced emf in a circuit is directly proportional to the time rate of change of magnetic flux linked with the circuit. Mathematically, it is expressed as: $$e = -\frac{d\Phi_B}{dt}$$\nWhere $\Phi_B$ is the magnetic flux and $e$ is the induced emf.

Lenz's Law:\nLenz's Law states that the direction of the induced current is always such that it opposes the cause (change in magnetic flux) that produces it. The negative sign in Faraday's equation represents Lenz's law.

Conservation of Energy:\nLenz's law is a direct consequence of the law of conservation of energy. When a magnetic pole is brought near a closed coil, the induced current produces a magnetic field that opposes the motion of the magnet (repulsion). To move the magnet against this repulsive force, external mechanical work must be done. This mechanical work is converted into electrical energy and subsequently into thermal energy (Joule heating) in the coil. If the induced current were in a direction to favor the motion, the magnet would accelerate without any external work, creating energy out of nothing, which violates the law of conservation of energy.