Question

If a coil of metal wire is kept stationary in a non-uniform magnetic field, then
(A) An e.m.f is induced in the coil
(B) A current is induced in the coil
(C) Neither e.m.f nor current is induced
(D) Both e.m.f and current is induced

Answer 1

Hint: In order to solve this question, we should know that magnetic flux through an area is the product of the magnetic field and area of that surface and this change in magnetic flux determines the e.m.f produced in any coil through it, here we will discuss and apply Lenz’s law to determine the correct answer.

Complete step by step solution:
Lenz’s law states that whenever there is a change in magnetic flux through the metallic object then an e.m.f is induced in it and therefore a current is also induced in the metallic object. and this e.m.f will only induce if and only if the magnetic flux changes with time.

It’s given that a coil of metal is placed stationary in a non-uniform magnetic field since the magnetic field is non-uniform but it’s not changing with time and also coil is kept stationary which means there is no change in the area of the coil passing through the magnetic field and hence there is no change in magnetic flux through the coil so, according to Lenz's law since no magnetic flux is changing with time through the coil hence neither e.m.f nor current will induced through the coil.

Hence, the correct answer is option (C) i.e, Neither e.m.f nor current is induced.

Note: It should be noted that mathematically the magnitude of e.m.f is given by $\left| e \right| = \dfrac{{d\phi }}{{dt}}$ where $e,d\phi $ are e.m.f and change in magnetic flux with respect to time and an e.m.f induced in a metallic coil only when there is a change in magnetic flux with time.