You are given the rectangular loop carrying I 2 A current in the counter clockwi

Question

You are given the rectangular loop carrying I2 A current in the counter clockwise(CCW) direction. The loop is in the magnetic field of a current line of I1 A (assumeinfinite current line). All numbers on the graph are in meters.

We would like to know if there is a torque on the loop (use the center of the loop as the pivot point). First, find if there is a torque on the loop using the forces that you found in part a? Then using magnetic moment of the loop and what you know about magnetic moments and torque verify the torque. Please show your work clearly.

Explanation / Answer

From the loop we can calculate L2 = L4 = 3

R2 = 3, R4 = 9

I1 = 11 A

I2 = 12A

The force due to wire on the rectangular wire is

Fnet = F1 + F2 + F3 + F4

= F1 + F2 + 0 + F4

= F2 + F4

The forces F2 and F4 in terms of I2 and B2 and B4 are

F2 =( I2 L2 x B2 ) i

= ( uo L2 * I1 * I2 / 2 * pi * R2 ) i

= (4*3.14 x 10-7 * 3 * 11*12 / 2*3.14 * 3)

= 0.264 x 10-4 i

F4 = (I2 L4 x B4) i

=  - ( uo L4 * I1 * I2 / 2 * pi * R4 ) i

= - (4*3.14 x 10-7 * 3 * 11*12 / 2*3.14 * 9)

= - 0.088 x 10-4 i

The net force Fnet = 0.264 x 10-4 i - 0.088 x 10-4 i = 0.176 x 10-4 i

Magnitude of net force | Fnet | =  0.176 x 10-4

Torque = force x distance

= (0.176 x 10-4 ) i x (-3i - 1.5j)

= ( -1.5 i + 0.264 x 10-4 k ) N-m

magnitude of net torque = 1.50 N-m

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