A uniform magnetic field exists in a square of side 2a (as shown in Fig). A square loop of side a centers the field along a diagonal and leave it at a constant speed. Draw the curve between induced emf e and distance along the diagonal, say `x_(0)`

Options

A.
B.
C.
D.

Answer

D

Explanation

The graph is to be drawn qualitatively

As shown, for `0 le x le a`
`phi=Bx^(2)`
`e=(-d phi)/(dt) =-2Bx*(dx)/(dt)=-2 Bxv`
At `x=0, e=0`
at `x=a//2, e=-Bav`
as, `x rarr a "but " != a, e~~-2 Bav`
As, `x=a, e=0` as `phi =` constant
Distance along diagonal `(x_0)=xsqrt(2)`, thus, `x_(0)=f(x)`
When the loop reaches completely inside the field, it starts coming out of the field after some moment. When the loop is coming out, `(x_1)` should be selected carefully, for which
`phi=(B)(a-x_(1))^(2)`
`e=(-dphi)/(dt)=-2B(a-x_(1))*(v)`
`=2B(a-x_(1))v`
`x_(1)=a, e=0`
Thus, before the loop enters the field completely, `e= -2 Bav`. When the loop is completely inside the field `e=0 (phi=`constant). as the loop starts coming out of the field `(e=2Bav)`. option (d) is correct.