Question

A circular coil of n turns and radius R carries a current I. It is unwound and rewound to make

another square coil of side a keeping number of turns and current same. Calculate the ratio ofmagnetic moment of the new coil and the original coil.

Answer 1

The expression for magnetic moment of a current carrying coil is given as

m = NIA

here

N - number of turns

I - current flowing in the coil

A - cross-sectional area of coil

now,

for the circular coil [A = Ï€R²]

m = NI(Ï€R²)

and

for the square coil [A = a x a = a²]

m' = NI(a²)

thus, the ratio of magnetic moment will be

m' / m = [ NI(Ï€R²)] / [NI(a²)]

thus,

m' / m = Ï€R² / a²