Question

Calculate the magnetic field strength needed on a 200-turn square loop 20.0 cm on a side to create a maximum torque of 300 N⋅m if the loop is carrying 25.0 A.

a) 0.30 T
b) 0.40 T
c) 0.50 T
d) 0.60 T

Answer 1

To calculate the magnetic field strength needed to create a maximum torque on a square loop carrying a current, we can use the formula Torque = N * B * A * sin(theta), where N is the number of turns, B is the magnetic field strength, A is the area of the loop, and theta is the angle between the magnetic field and the normal to the loop. Given the values provided, the magnetic field strength needed is 0.375 T.

Step-by-step explanation:

To calculate the magnetic field strength needed to create a maximum torque, we can use the formula:

Torque = N * B * A * sin(theta)

Where N is the number of turns in the loop, B is the magnetic field strength, A is the area of the loop, and theta is the angle between the magnetic field and the normal to the loop. In this case, we can assume that theta is 90 degrees, so sin(theta) = 1. Given that the loop has 200 turns, an area of (20.0 cm)^2 = 400 cm^2, and a current of 25.0 A, we can rearrange the formula to solve for B:

B = Torque / (N * A * sin(theta)) = 300 N*m / (200 * (20.0 cm)^2 * 1) = 0.375 T

Therefore, the magnetic field strength needed is 0.375 T.