Question

Two concentric current loops lie in the same plane. The smaller loop has a radius of 2.9 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.
What is the radius of the bigger loop?

Answer 1

Answer:

the radius of bigger loop is 4.83cm

Explanation:

Given that,

two concentric current loops

smaller loop radius = 2.9 cm

current in smaller loop = 12 A

current in the bigger loop = 20 A

magnetic field at the center of loop = 0

Radius of the bigger loop = ?

The equation for the magnetic field at the center of a circular loop is:

$B=\frac{\mu_0I}{2R}$

we have:

$B = B_1 + B_20 = \dfrac{\mu_0I_1}{2R_1} +\dfrac{\mu_0I_2}{2R_2}$

now,

$\dfrac{I_1}{R_1} = \dfrac{I_2}{R_2}R_2 = I_2\dfrac{R_1}{I_1} = 20\times \dfrac{2.9}{12} = 4.83 cm$

the radius of bigger loop is 4.83cm

Answer 2

Answer:

The radius is 4.833cm

Explanation:

The image will provide a better clarification of the explanation