Question

There is a loop with a radius of R, on the xy plane. The non-uniform time dependent magnetic field is $B(s,t) = \frac{1}{s} B_{_{o}} t^{2}\hat{z}$

What is the electric field in the wire, and at what direction?

Answer 1

A loop with radius R on the xy - plane A non uniform time dependent magnetic field is B^rightarrow (s, t) = 1/s B_) t^2 z6 cap In figure the z^cap is pointed out from the plane of paper Now flux through the loop is phi = integral B^rightarrow middot dA = integral 1/s B_0 t^2 z^cap middot dx dy z^cap phi = B_0 t^2/s middot pi R^2 - so emf induced on the loop is epsilon = -d phi/dt = -d/dt (B_0 t^2/2 pi R^2) epsilon = 2 B_0 t/s pi R^2 = -2 pi b_0 R^2/2 t - Hence electrical field at point due to induced emf is e6 rightarrow = -partial difference epsilon/ partial difference s s^cap E^rightarrow = partial difference/ partial difference s(- z pi B_0 R^2 t/s)S^cap = 2 pi B_0 R^2 t partial difference/ partial difference s(S^- 1)S^cap