Question

As a result of change in the magnetic flux linked to the closed loop as shown in the figure, an e.m.f. V volt is induced in the loop. The work done (joule) in taking a charge Q coulomb once along the loop is

• A. QV
• B. 2QV
• C. QV/2
• D. zero.

Answer 1

The Correct Option is A

To solve this problem, we need to understand the relation between the induced electromotive force (EMF) and the work done in moving a charge around the loop.

The problem states that an EMF of V volts is induced in the loop. According to Faraday's law of electromagnetic induction, the EMF induced in a closed loop is equal to the negative rate of change of magnetic flux linkage through the loop. However, for this problem, we only need to focus on the EMF value provided.

The work done (W) in moving a charge (Q) around the loop when an EMF (V) is induced is given by the basic formula:

W = QV

Let's analyze this with the given options:

1. QV: This directly matches the derived formula for work done using charge and induced EMF.
2. 2QV: This is twice the calculated work done, which is not applicable here.
3. \frac{QV}{2}: This is half the calculated work done, which is not applicable here.
4. zero: This is incorrect because work is performed when a charge is moved in presence of EMF.

Therefore, the correct answer is QV, as it perfectly aligns with the formula for work done by an induced EMF in moving charge Q around a loop.