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

Answer:

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.

$B= \frac{\mu_0 I}{2r}$

The magnetic field at the center of the smaller loop;

$B_1 = \frac{\mu_0 I_1}{2 r_1}$

The magnetic field at the center of the bigger loop;

$B_2 = \frac{\mu_0 I_2}{2 r_2}$

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

$B_1 = B_2 = \frac{\mu_0 I_1}{2 r_1} = \frac{\mu_0 I_2}{2 r_2} \\\\\frac{I_1}{ r_1} = \frac{ I_2}{r_2} \\\\r_2 = \frac{I_2 r_1}{ I_1} = \frac{(20 \ A) \times (3.0 \ cm)}{12 \ A} = 5 \ cm$

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