Question

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?

Answer 1

the radius of the bigger loop is 5 cm.

Step-by-step 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.

`B= (\mu_0 I)/(2r)`

The magnetic field at the center of the smaller loop;

`B_1 = (\mu_0 I_1)/(2 r_1)`

The magnetic field at the center of the bigger loop;

`B_2 = (\mu_0 I_2)/(2 r_2)`

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

`B_1 = B_2 = (\mu_0 I_1)/(2 r_1) = (\mu_0 I_2)/(2 r_2) \\\\(I_1)/( r_1) = ( I_2)/(r_2) \\\\r_2 = (I_2 r_1)/( I_1) = ((20 \ A) * (3.0 \ cm))/(12 \ A) = 5 \ cm`

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