Two concentric current loops lie in the same plane. The smaller loop has a radius of 3.0 cm and a current of 12 A. The bigger loop has a current of 20 A. The magnetic field at the center of the loops is found to be zero. Required:
What is the radius of the bigger loop?

the radius of the bigger loop is 5 cm.

Explanation:

Given;

current in the smaller loop, I₁ = 12 A

current in the larger loop, I₂ = 20 A

radius of the smaller loop, r₁ = 3 cm

let the radius of the larger loop, = r₂

Apply Biot-Savart's law to determine the magnetic field at the center of the circular loops.

The magnetic field at the center of the smaller loop;

The magnetic field at the center of the bigger loop;

If the magnetic field at the center is zero, then B₁ = B₂

Therefore, the radius of the bigger loop is 5 cm.