The figure shows two concentric metal loops, each carrying a current. The larger loop carries a current of 8.0 A and has a radius of 0.060 m. The smaller loop has a radius of 0.040 m. What is the value of a current in the smaller loop that will result in zero total magnetic field at the center of the system?

Question

Quizplus · Accepted Answer

At the center of the system, the magnetic field due to the larger loop and the smaller loop should be equal and opposite to each other. Using the formula for the magnetic field at the center of a circular loop, we can set up an equation:

B = μ0I/2R

For the larger loop, with a radius of 0.060 m and a current of 8.0 A, the magnetic field at the center is:

B1 = (4π×10^-7 T m/A)(8.0 A)/(2×0.060 m) = 2.11×10^-5 T

For the smaller loop, let's assume the current is I. The distance from the center to the smaller loop is 0.020 m. The magnetic field at the center due to the smaller loop is:

B2 = (4π×10^-7 T m/A)(I)/(2×0.020 m) = 1.26×10^-5 I T

For the total magnetic field at the center to be zero, we need:

B1 = -B2

2.11×10^-5 T = -1.26×10^-5 I T

Solving for I, we get:

I = 5.3 A

The Figure Shows Two Concentric Metal Loops, Each Carrying a Current