Question

State Lenz’s law and explain how this law is a consequence of conservation of energy principle.

Answer 1

Lenz’s Law

Statement: Lenz’s Law states that:

"The direction of the induced current in a closed conducting loop is such that it always opposes the change in magnetic flux that produced it."

Mathematical Expression:

\[ \mathcal{E} = -\frac{d\Phi_B}{dt} \]

• \( \mathcal{E} \) is the induced electromotive force (emf)
• \( \Phi_B \) is the magnetic flux through the loop
• The negative sign indicates opposition to the change in flux

Explanation: Consequence of Conservation of Energy

• The negative sign in Lenz's Law ensures that the induced current creates a magnetic field opposing the change in the original magnetic field.
• If the induced current supported the change instead of opposing it, it would amplify the magnetic flux.
• This would result in a positive feedback loop, where the current increases indefinitely without an external energy source.
• Such a scenario would violate the law of conservation of energy, as it would imply creation of energy from nothing.
• By opposing the change, the induced current ensures that work is done against the opposing magnetic field, converting mechanical energy into electrical energy.

Conclusion:

Lenz’s Law is not only a fundamental rule of electromagnetism but also a direct consequence of the principle of conservation of energy. It ensures that energy is neither created nor destroyed in the process of electromagnetic induction.