Question

A single-turn current loop, carrying a current of 4.39 A, is in the shape of a right triangle with sides 67.2, 152, and 166 cm. The loop is in a uniform magnetic field of magnitude 102 mT whose direction is parallel to the current in the 166 cm side of the loop. What is the magnitude of the magnetic force on (a) the 166 cm side, (b) the 67.2 cm side, and (c) the 152 cm side? (d) What is the magnitude of the net force on the loop?

Answer 1

The magnitude of the magnetic force on each side of the current loop can be calculated using the equation F = ILB, where I is the current, L is the length of the side, and B is the magnitude of the magnetic field. The magnitude of the magnetic force on the 166 cm side is 7.16 N, on the 67.2 cm side is 3.05 N, and on the 152 cm side is 6.32 N. The magnitude of the net force on the loop is 0 N.

Step-by-step explanation:

To find the magnitude of the magnetic force on each side of the current loop, we can use the equation for the magnetic force on a straight current-carrying wire, which is given by the cross product of the current and the magnetic field. The magnitude of the magnetic force on a side of length L is given by F = ILB, where I is the current, L is the length of the side, and B is the magnitude of the magnetic field.

(a) The magnitude of the magnetic force on the 166 cm side is F = (4.39 A)(166 cm)(0.102 T) = 7.16 N.

(b) The magnitude of the magnetic force on the 67.2 cm side is F = (4.39 A)(67.2 cm)(0.102 T) = 3.05 N.

(c) The magnitude of the magnetic force on the 152 cm side is F = (4.39 A)(152 cm)(0.102 T) = 6.32 N.

(d) To find the magnitude of the net force on the loop, we can add up the magnitudes of the forces on each side. The net force on the loop is the vector sum of the forces on each side, but since the forces on opposite sides are equal and opposite in direction, the net force is equal to zero. Therefore, the magnitude of the net force on the loop is 0 N.