A circular coil lies in the plane of this page and has 25 tu

A circular coil lies in the plane of this page and has 25 turns, a radius of 6.00 cm, and a total resistance of 1.80 Ohm. A magnetic field is directed into this page at an angle of 40.0 degree from the perpendicular to the plane of the coil. If the magnitude of the magnetic field varies in time according to the relationship B(t) = (50.0 mT/s^2) t^2 = (20.0 mT/s) t, then Find the induced current in the coil at t = 0.500 s. In what sense does the induced current circulate, clockwise or counterclockwise?

Solution

Here ,

B = 50 t^2 + 20 t

R = 1.80 Ohm

N = 25

radius ,r = 0.06 m

theta = 40 degree

a) dB/dt = d/dt(50 t^2 + 20 t)

dB/dt = 100 * t + 20

for the induced current

I = dB/dt * pi *r^2 * N * cos(theta)/R

at t = 0.5 s

I = (100 * 0.5 + 20) * pi * 0.06^2 * 25 * cos(40 degree)/1.80

I = 8.423 mA

the induced current in the loop is 8.423 mA

b)

as the applied magnetic field is into the page
induced magentic field is out of the page

the sense of induced current will circulate is counterclockwise