Question

A circular loop in the plane of the paper lies in a 0.78 T magnetic field pointing into the paper.

A) If the loop's diameter changes from 16.6 cm to 6.4 cm in 0.63 s , what is the direction of the induced current? Clockwise or Counterclockwise?

B) What is the magnitude of the average induced emf? Answer in V.

C) If the coil resistance is 4.3 ohm , what is the average induced current? Answer in A

Answer 1

Given magnetic field   B = 0.78 T

Initial diameter d1 = 16.6 cm = 0.166 m

radius r1 = 0.166 / 2 = 0.083 m

Area of cross section   A1 = pi * (r1)^2

A1 = pi * (0.083)^2 = 0.0216 m^2

Final diameter    d2   = 6.4 cm = 0.064 m

radius r2 = 0.064 / 2 = 0.032 m

Area of cross section   A2 = pi * (r2)^2

A2 = pi * (0.032)^2 = 0.0032 m^2

A)

As the area of cross section decreases the induced current should create a magnetic field in the direction of orginal magnetic field so

The Induced current should be in Clockwise direction

B)

Induced emf   e = - d(?) / dt

e = - d(B*A) / dt

e = - B * dA / dt

here dA = A2 - A1 = 0.0032 - 0.0216 = -0.0184

time interval    dt = 0.63 s

therefore   e = - 0.78 * (-0.0184) / 0.63

e = 0.0228 V   = 2.28 * 10^-2 V

C)

Induced current I = e / R

I = 0.0228 / 4.3

I = 0.0053 A

I = 5.3 * 10^-3 A