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: 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: Thus, Lenz’s Law is a direct consequence of the Law of Conservation of Energy.