Question

State Lenz’s Law. Show that it is a consequence of the Law of Conservation of Energy.

Hint:

Lenz’s Law prevents creation of energy from nothing. Opposition of induced current ensures energy conservation.

Answer 1

Concept: Lenz’s Law describes the direction of induced current in electromagnetic induction and ensures that energy is conserved during the induction process. 
Statement of Lenz’s Law: Lenz’s Law states that: \begin{quote} The direction of induced current in a circuit is such that it opposes the change in magnetic flux that produces it. \end{quote} Mathematically, it is represented by the negative sign in Faraday’s law: \[ \mathcal{E} = -\frac{d\Phi}{dt} \] Relation with Conservation of Energy: To show that Lenz’s Law follows from conservation of energy, consider the following situation.
Case: Magnet approaching a coil 
Step 1: Change in magnetic flux When a bar magnet is moved towards a coil: 
Magnetic flux linked with the coil increases. 
An emf and current are induced in the coil. 
Step 2: Direction of induced current According to Lenz’s Law: 
The induced current produces a magnetic field opposing the approaching magnet. 
The face of the coil near the magnet behaves like a similar pole (repulsion). 
Step 3: Work done by external agent Because of opposition: 
An external force is required to push the magnet towards the coil. 
Mechanical work is done. 
This mechanical energy is converted into: 
Electrical energy in the coil 
Heat due to resistance (Joule heating) 
If Lenz’s Law were not true: If the induced current aided the motion: 
The magnet would accelerate automatically. 
Electrical energy would be produced without external work. 
This would violate the law of conservation of energy. 
Conclusion: Since the induced current always opposes the cause producing it, external work is required, ensuring that: \[ \text{Mechanical energy} \rightarrow \text{Electrical energy} \] Thus, Lenz’s Law is a direct consequence of the Law of Conservation of Energy.