Question

As a result of change in the magnetic flux linked to the closed loop shown in the fig, 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. $\dfrac{{QV}}{2}$
C. $2QV$
D. Zero

Answer 1

Hint:This question utilizes the concept of Biot - Savart’s law. This law gives the relationship between current and the magnetic field induced by it. Here, an external magnetic field induces an e.m.f. $V$ in the loop. Then the work done to move a charge $Q$ along the loop in presence of $V$ is found out.

Formulae used:
$V = \dfrac{W}{Q}$
where $V$ is the ElectroMotive Force or the e.m.f., $W$ is the work done and $Q$ is the Charge.

Complete step by step answer:

According to the given question, charge present in the loop is $Q$ and E.m.f. induced by an external magnetic field is $V$. We know that the induced electric field due to change in magnetic field is non – conservative in nature. That is, the value of the Electric field is path dependent. Thus, the work done in overcoming that field cannot be zero.Using the formulae
$V = \dfrac{W}{Q}$
we get
$ \Rightarrow W = QV$

Therefore, the correct option is A.

Note:If the electric field was conservative in nature, that is not dependent on the path, the answer would have been zero. But since the electric field due to the changing magnetic field is dependent on the path taken, we get a non-zero answer.