A square loop of side 'a' is placed in `x-y` plane as shown in figure. In this region there is non-uniform time dependent magnetic field `vec B= (cy^3 t^2) veck`, [where t is time and c is constant] then magnitude of emf induced in loop is

Options

A. Zero
B. `(ca^(4)t^(2))/5`
C. `(ca^(5)t)/2`
D. data is insufficient

Explanation

`phi=intvec(B).vec(dA)`
`phi=int cy^(3) t^(2) a dy `
`phi=ct^(2). A int_(0)^(a) y^(3) dy`
`phi=ct^(2)a.(a^(4))/4`
`phi=(ct^(2)a^(5))/4`
`e=|-(dvarphi)/(dt)|`
Now induced e.m.f.
`e=|-(2cta^(5))/4|=(2cta^(5))/4=(cta^(5))/2`