Two concentric circular wire loops in the same plane each carry a current. The larger loop has a current of 8.46 A circulating clockwise and has a radius of 6.20 cm. The smaller loop has a radius of 4.42 cm. What is the magnitude and direction of the current in the smaller loop if the total magnetic field at the center of the system is zero?
A) 6.03 A CCW
B) 6.03 A CW
C) 12.8 A CCW
D) 12.8 A CW

Question

Quizplus · Accepted Answer

The magnetic field at the center of each loop due to its own current is directly proportional to the current in the loop and inversely proportional to the radius of the loop. For the total magnetic field at the center to be zero, the magnetic fields due to both loops must be equal in magnitude but opposite in direction. Since the larger loop's current is clockwise, the smaller loop's current must be counterclockwise to oppose the magnetic field of the larger loop. Using the formula for the magnetic field due to a current in a loop, $B = \frac{\mu_0 I}{2R}$, and setting the fields equal to each other with the currents in opposite directions, we can solve for the current in the smaller loop, which gives us 6.03 A counterclockwise.

Two Concentric Circular Wire Loops in the Same Plane Each