Question

A 200-turn circular loop with a current of 100 A is in the Earth's field. What is the direction and magnitude of the torque when viewed from the east?

a) 1.50 × 10-2 N. m clockwise
b) 2.25 × 10-2 N. m clockwise
c) 1.50 × 10-2 Nm counterclockwise
d) 2.25 × 10-2 Nm counterclockwise

Answer 1

The torque on the circular loop is 1.50x10^-2 Nm and it is clockwise when viewed from the east due to the Earth's magnetic field.

Step-by-step explanation:

The torque on a circular loop due to the Earth's magnetic field can be calculated using the equation T = NIA sinθ, where T is the torque, N is the number of turns in the loop, I is the current, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop. In this case, the loop has 200 turns, a current of 100 A, a radius of 50.0 cm, and the Earth's field is due north. Since the Earth's field is parallel to the ground, θ would be 90° when viewed from the east. Therefore, the torque on the loop can be calculated as:

T = (200)(100)(π(0.5)^2)(3.00x10^-5)sin(90°) = 1.50x10^-2 Nm

The direction of the torque can be determined by using the right-hand rule. If you point your thumb in the direction of the current (clockwise when viewed from the east), and your fingers in the direction of the magnetic field (north), then your palm will be facing downward. Therefore, the torque is clockwise when viewed from the east.