Question

A rectangular, a square, a circular and an elliptical loop, all in the $(x-y)$ plane, are moving out of a region of uniform magnetic field, with a constant velocity, $\overrightarrow{V}=v\hat{i}$. The magnetic field is directed along the negative $z-$ direction. The induced emf, during the passage of these loops out of the region of magnetic field, will not remain constant for:

• A. Any of the four loops
• B. The rectangular, circular and elliptical loops
• C. The circular and the elliptical loops
• D. Only the elliptical loop

Answer 1

The correct option is C The circular and the elliptical loops

We know that when magnetic field is constant and area is varying the induced emf is given by,

$E=-\frac{d\left(BA\right)}{dt}=-B\frac{dA}{dt}$

When all of the given loops are moving out of magnetic field, $\left(\frac{dA}{dt}\right)$ i.e. the rate at which the area is coming out of the field, for circular and elliptical loop is not constant through the magnetic field.

Therefore, the induced emf is also not constant through the circular and the elliptical loops.

Hence, option ($C$) is the correct answer.

Why this Question? Note: According to Faraday's law, the induced e.m.f is given by, $E=-\frac{d\left(BA\right)}{dt}$ If $B$ is constant, then $E=-B\frac{dA}{dt}$