MP Board · Class 12 · Physics · Electromagnetic InductionState Faraday's laws of electromagnetic induction. State Lenz's law and explain clearly with an example how Lenz's law is a consequence of the law of conservation of energy.

Electromagnetic Induction and Lenz's Law

1. Faraday's Laws of Electromagnetic Induction

• 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 flux continues.
• Second Law: The magnitude of the induced electromotive force (emf) in a circuit is directly proportional to the time rate of change of magnetic flux linked with the circuit. $$\varepsilon \propto \frac{d\Phi_B}{dt} \implies \varepsilon = -\frac{d\Phi_B}{dt}$$ (Where the negative sign indicates the direction of induced emf according to Lenz's law.)

2. Lenz's Law\nLenz's law states that the direction of the induced current (or induced emf) in a circuit is always such that it opposes the change in magnetic flux that produces it.

$$\varepsilon = -N \frac{d\Phi_B}{dt}$$

3. Explanation of Lenz's Law as Conservation of Energy\nLenz's law is a direct consequence of the Law of Conservation of Energy.

Case Study: Moving a Bar Magnet Towards a Closed Coil

1. Approaching the North Pole:

   • When the North pole ($N$) of a bar magnet is moved towards a closed coil, the magnetic flux linked with the coil increases.
   • According to Lenz's law, the induced current in the coil flows in an anticlockwise direction (as seen from the magnet's side), creating an induced North pole on the face of the coil facing the magnet.
   • Like poles repel each other. Therefore, a force of magnetic repulsion opposes the inward motion of the magnet.

2. Mechanical Work Converted to Electrical Energy:

   • To keep the magnet moving towards the coil, an external mechanical force must do work against this repulsive force.
   • This mechanical work done by the external agent is converted into electrical energy in the coil, which eventually dissipates as heat energy (Joule heating).

3. Withdrawing the North Pole:

   • Conversely, when the North pole is moved away from the coil, the magnetic flux decreases.
   • The induced current now flows in a clockwise direction, creating a South pole on that face, attracting the magnet and opposing its outward motion.
   • Work must again be done against this attractive magnetic force.

What if Lenz's Law Were Violating Energy Conservation?

• Suppose the induced current aided the motion (e.g., creating a South pole when the North pole approaches).
• The magnet would be attracted and accelerated towards the coil without any external effort, gaining continuous kinetic energy and generating electrical energy simultaneously out of nothing.
• This would create energy from nowhere, violating the First Law of Thermodynamics (Law of Conservation of Energy).

Conclusion:\nThus, Lenz's law strictly adheres to the principle of conservation of energy. Mechanical energy spent in overcoming magnetic resistance is transformed into electrical and thermal energy.