NCERT · Class 12 · Physics · Electromagnetic InductionState Faraday's laws of electromagnetic induction. State Lenz's law and explain in detail how Lenz's law is a direct consequence of the law of conservation of energy.

Faraday's Laws of Electromagnetic Induction

1. First Law: Whenever there is a change in the magnetic flux linked with a closed circuit, an electromotive force (emf) is induced in the circuit. This 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. $$ e \propto \frac{d\Phi_B}{dt} \implies e = -k \frac{d\Phi_B}{dt} $$\nIn SI units, $k = 1$, so: $$ e = -\frac{d\Phi_B}{dt} $$ (The negative sign represents the direction of induced emf according to Lenz's law).

Lenz's Law

Statement: The direction of induced current in a circuit is always such that it opposes the cause (or change in magnetic flux) that produces it. $$ e = -\frac{d\Phi_B}{dt} $$

Lenz's Law and Conservation of Energy\nLenz's law is a direct consequence of the Law of Conservation of Energy. This can be understood as follows:

1. Mechanical Work into Electrical Energy:

   • When the North pole ($N$-pole) of a bar magnet is moved towards a closed coil, the induced current flows in such a direction that the front face of the coil acts as a North pole.
   • Like poles repel each other. Therefore, a repulsive force opposes the inward motion of the magnet.
   • To move the magnet closer against this repulsive force, external mechanical work must be done.
   • This mechanical work done against the magnetic repulsion is converted into electrical energy, which appears as induced current and subsequent heat energy in the circuit.

2. Consequence if Lenz's Law were False:

   • Suppose the induced current produced an South pole ($S$-pole) instead. The magnet would then be attracted towards the coil automatically, accelerating without any external work.
   • This would create electrical energy continuously out of nothing, violating the Law of Conservation of Energy. \nHence, Lenz's law complies strictly with the principle of energy conservation.