Question

A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicularly to the plane of the coil. The radius of the coil changes as shown in the diagram. The graph of the magnitude of induced emf in the coil is represented by

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

In the r-t graph, it is clear that from a to $b$ there is no change in radius and hence no change in area and magnetic flux. Same is the situation from c to $d$ for $b$ to $c$.
Now, $|e|=\frac{d}{dt}(\varphi )$
$|e|=B\frac{d}{dt}\left(\pi (r{)}^2\right)=B\pi 2r\frac{dr}{dt}$
Since $r\propto t,$
$\therefore \frac{dr}{dt}=$ constant
$\therefore |e|\propto r$
This is represented in option (2).