Question

A 22-turn circular coil of radius 5.00 cm and resistance 1.00 ? is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.010 0t + 0.040 0t², where B is in teslas and t is in seconds. Calculate the induced emf in the coil at t = 5.40 s.
mV

Answer 1

total flux through the coil = N*B*A

N = number of turns

B = magnetic field = 0.01t + 0.04t^2

A = area= pi*r^2 = 3.14*0.05*0.05 = 0.00785 m^2

N = 22

lenz law :The direction of motion induced emf is always such that it opposes the rate of change in flu

emf = -rate of change in flux

emf = (d/dt)*flux

emf = (d/dt)*N*B*A

here A,N is constant

emf = N*A*(dB/dt)

dB/dt = 0.01 + 2*0.04*t

at t= 5.4 s

dB/dt = 0.01+(2*0.04*5.4) = 0.442

emf = N*A*dB/dT

emf = 22*0.00785*0.442 = 0.0763334 v = 76.33 mv <---answer

indued current = emf / Resistance =
76.33 milli ohms <-answer