Question

A 28-turn coil with a diameter of 6.00 cm is placed in a constant, uniform magnetic field of 1.00 T directed perpendicular to the plane of the coil. Beginning at time

t = 0 s,

the field is increased at a uniform rate until it reaches 1.30 T at

t = 10.0 s.

The field remains constant thereafter. What is the magnitude of the induced emf in the coil at the following times?

(a)    t < 0 s
mV

(b)    t = 5.00 s
mV

(c)    t > 10.0 s
mV

Answer 1

Given

number of turns are N = 28

diameter d = 0.06 m , radius r = 0.03 m

magnetic field B = 1 T

at t= 0s , B1 = 1 T  

later at t = 10s , B2 = 1.30 T

induced emf = -dphi/dt

emf = -d(B*A*N cos theta) /dt

emf = -d(B*A*N*cos0)/dt

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

emf = - A*N (dB/dt)

emf = pi*r^2*dB/dt

emf = pi*0.03^2*0.3*28/10 V  

emf = 0.0023750440461 V = 2.375 mV

at t < 0 there is no change in magnetic field so the emf = 0 mV

and after t > 10 s the magnetic field is not varying so the induced emf = 0 mV