A square coil of wire of side 340 cm is placed in a uniform

A square coil of wire of side 3.40 cm is placed in a uniform magnetic field of magnitude 2.25 T directed into the page as in the figure shown below. The coil has 23.0 turns and a resistance of 0.780 . If the coil is rotated through an angle of 90.0° about the horizontal axis shown in 0.335 s, find the following.

(a) the magnitude of the average emf induced in the coil during this rotation
mV

(b) the average current induced in the coil during this rotation
mA

Solution

magnetic flux through the coil = N*B*A*costheta

induced emf = rate of change in flux

induced emf = N*B*A*(costheta1 - costheta2)/t

theta1 = 0

theta2 = 90

t= time= 0.335 s

A = area of square = 0.034^2

B = magnetic field = 2.25 T

induced emf = 23*2.25*0.034^2*(cos0 - cos90)/0.335

induced emf e = 0.178 V = 178 mV

=========================

part (b)

current I = e/R

resistance R = 0.78 ohm

I = 178/0.78

current I = 228.2 mA