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

The cross sectional area of a wire is given by `pi r ^(2)` where r is the radius of the wire.
The emf induced in the wire is given by
`|epsi| = (d phi )/( dt ) = B ( dA)/(dt) = B (d)/(dt) ( pi r ^(2))= 2 pi Br (dr)/(dt)`
i.e., `epsi prop r ( dr)/(dt)`
At `t = (0-1) s, (dr)/(dt) = 0. so epsi =0`
The induced emf will be zero
At `t = (1-2) s, (dr)/(dt) = ` constant
so `epsi prop r`
The graph will reise linearly.
At `t gt 2 s. (dr)/(dt) = 0. so epsi = 0`
The curve will fall steeply to zero.