Question

Two concentric current loops lie in the same plane. The smaller loop has a radius of 2.7cm 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:

Radius of bigger loop(R) =4.5cm

Explanation:

Consider a circular path of radius r around the wire.  The magnetic field along that path is given by ;

∫B*dl = k*I where I is the current enclosed.  From symmetry, ∫B*dl = 2*π*r*B

B = K*I/r, so the magnetic field varies inversely as the loop radius and directly as the current.

The smaller loop current to radius ratio is  12/2.7

The bigger loop current to radius ratio is = 20/R

12/2.7 = 20/R

R = (20 * 2.7)/12

R=54/12

R=4.5cm

Answer 2

Answer:

Explanation:

The B-field at the center of a circular loop of radius, r and current, I is;

Magnetic field, B = (μ × I) ÷ 2pi × R

Given:

rs = 2.7 cm

= 0.027 m

Is = 12 A

Ib = 20 A

(μ × Is)/2 × rs = (μ × Ib)/2 × rb

Inputting values,

rb = (20 × 2 × 0.027)/12 × 2

= 0.045 m

= 4.5 cm.