Question

A circular loop of wire with radius 3 m is flat on the xy plane in a magnetic field which is pointed in the z-direction and has a magnitude of 5 μT. What is the magnitude of the induced emf in the loop if the loop shrinks to a radius of 1.5 m in 3 seconds?

Group of answer choices a) 1.06e-4 V b) 3.53e-5 V c)None of the above d) 7.85e-6 V e) 0 V

Answer 1

Induced EMF in a loop placed in magnetic field is given by:

EMF = -N*d/dt

= Magnetic flux = B*A*cos

EMF = N*d(B*A*cos )/dt

EMF = N*B*cos *dA/dt

N = number of loops = 1

B = Magnetic field = 5*10^-6 T in z-direction

dt = time interval = 3 sec

dA = Change in area = Af - Ai = pi*(rf^2 - ri^2)

= Angle between magnetic field and Area vector = 0 deg, (since loop is placed in xy plane, So area vector is in z direction)

So,

EMF = -N*B*cos *pi*(rf^2 - ri^2)/dt

EMF = -1*5*10^-6*cos 0 deg*pi*(1.5^2 - 3.0^2)/3

EMF = 3.53*10^-5 V = 3.53e-5 V

Correct option is B.