Question

Which of the following statements is not correct for electromagnetic induction?

• A. The magnitude of induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit.
• B. The magnitude of induced emf in a circuit is equal to the total change of magnetic flux through the circuit.
• C. The induced emf can be increased by increasing the number of turns N of a closed coil.
• D. The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it

Hint:

The key term in Faraday's Law is "rate of change." Many incorrect statements will omit the "rate" part and just mention the "change" in flux. Always look for the dependence on time (\(d/dt\) or \(\Delta/\Delta t\)).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question tests the fundamental laws of electromagnetic induction: Faraday's Law and Lenz's Law. We need to identify the statement that incorrectly describes these principles.

Step 2: Detailed Explanation:
1. The magnitude of induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit.
This is a direct statement of Faraday's Law of Induction, \(|\mathcal{E}| = \left|\frac{d\Phi_B}{dt}\right|\). The EMF is proportional to the rate of change of flux. This statement is correct.
2. The magnitude of induced emf in a circuit is equal to the total change of magnetic flux through the circuit.
This statement claims \(|\mathcal{E}| = |\Delta\Phi_B|\). This is incorrect. The induced EMF depends on how quickly the flux changes (the rate, \(\Delta\Phi_B / \Delta t\)), not just the total change in flux. A large change in flux that happens very slowly will induce a very small EMF. This statement is not correct.
3. The induced emf can be increased by increasing the number of turns N of a closed coil.
For a coil with N turns, Faraday's Law is written as \(|\mathcal{E}| = N \left|\frac{d\Phi_B}{dt}\right|\). The total EMF is the sum of the EMFs induced in each turn. Therefore, increasing the number of turns \(N\) directly increases the total induced EMF. This statement is correct.
4. The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.
This is a precise statement of Lenz's Law, which determines the direction of the induced current and the polarity of the induced EMF. This statement is correct.

Step 3: Final Answer:
The question asks for the statement that is not correct. Statement (2) is a factually incorrect description of electromagnetic induction.