Question

A plane loop of wire enclosing an area of 4.90 cm² and having a resistance of 1.0 *10^-3 Ω is placed inside a long solenoid. The plane of the loop makes an angle of 60° with the solenoid's axis. The solenoid has 113 turns per cm of length, and at some instant carries a current of 5.0 A. The current is increasing at the rate of 2.8 103 A/s. Find the torque on the loop.

Correct answer is .000293 N*m

Answer 1

for the solenoid :

n = number of turns per unit length = 113 per cm = 11300 per m

i = current in solenoid = 5 A

magnetic field inside the solenoid is given as

B = ni

B = (12.56) (11300) (5 ) = 0.071T

rate of change of magnetic field is given as

dB/dt = n (di/dt)

A = area of the loop = 4.90 x 10^-4 m²

induced emf in the loop is given as

E = A(dB/dt) = nA (di/dt)

induced current in the loop is given as

i = E/R = nA (di/dt)/R = (12.56 x 10^-7) (11300) (4.90 x 10^-4) (2.8 x 10³)/0.001 = 19.5 A  

Torque is given as

= i A B Cos60

= (19.5) (4.90 x 10^-4) (0.071) Cos60

= 0.000339