A flat circular coil of 200 turns and radius 15 cm is placed with its plane perpendicular to the axis of a non-uniform magnetic field that is directed along the same axis. The magnitude of the field varies with radial distance r from the axis and with time t according to
B(r,t)=Art2,
where A=0.030Tm−1s−2.
(i) Obtain an expression for the total magnetic flux linked with the entire coil as a function of time.
(ii) Hence calculate the magnitude of the induced emf in the coil at t=0.10s.