Question

Two circular coils of current-carrying wire have the same magnetic moment. The first coil has a radius of 0.092 m, has 144 turns, and carries a current of 4.5 A. The second coil has 166 turns and carries a current of 9.3 A. What is the radius of the second coil?

Answer 1

Given N1I1A1 = N2 I2 A2

A2 /A1 = [N1/N2]* [I1/I2] = [144/166]*[4.5/9.3] = 0.4197

(r2/r1)^2 = 0.4197

. r2/r1 = 0.6479

r2 = 0.6479r1 = 0.6479*0.092 = 0.0596 m

Answer 2

Magnetic moment NI A.
N - number of turns
I - current
A- area of the circle.

Given N1 I1 A1 = N2 I2 A2

A2 /A1 = [N1/N2]* [I1/I2] = [144/166]*[4.5/9.3] = 0.4197

(r2/r1)^2 = 0.4197

. r2/r1 = 0.6478

r2 = 0.6478 r1 = 0.6478*0.092 = 0.0596 m

Answer 3

Magnetic moment NI A.
N - number of turns
I - current
A- area of the circle.

Given N1I1A1 = N2 I2 A2

A2 /A1 = [N1/N2]* [I1/I2] = [144/166]*[4.5/9.3] = 0.419

(r2/r1)^2 = 0.419

. r2/r1 = 0.647

r2 = 0.647r1 = 0.647*0.092 = 0.0596 m