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

Options

A.
B.
C.
D.

Answer

B

Explanation

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`.
Now, `|e|=(d)/(dt)phi`
`|e|=B(d)/(dt)(pir^(2))`
`|e|=2pirB(d)/(dt)`
Since `rpropt,implies(dr)/(dt)=constant`
`:.|e|propr`.
from `0-1,r` is constant, `:.(dr)/(dt)=0` hence, `e=0`
from `1-2, r=alphat`. :.(dr)/(dt)=0` hence `e=0`