Question

A 173 ‑turn circular coil of radius 2.79 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 11.9 Ω resistor to create a closed circuit. During a time interval of 0.161 s, the magnetic field strength decreases uniformly from 0.673 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.

energy:____________ mJ

Answer 1

n = number of turns = 173

r = radius of the coil = 2.79 cm = 0.0279 m

Area of cross-section of the coil is given as

A = r2 = (3.14) (0.0279)2 = 0.00244 m2

B = change in magnetic field = final magnetic field - initial magnetic field = 0 - 0.673 = - 0.673 T

t = time interval = 0.161 s

Induced emf in the circuit is given as

e = - n B A/t

e = - (173) (- 0.673) (0.00244)/(0.161)

e = 1.765 volts

R = resistance of the resistor = 11.9 Ω

i = current flowing through the resistor

Using Ohm's law

i = e/R = 1.765/11.9 = 0.15 A

U = energy dissipated in the resistor

Energy dissipated is given as

U = i2 R

U = (0.15)2 (11.9)

U = 0.26775 J

U = 267.75 mJ