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

magnetic moment (u) = NIA

where,
N - no of turns
I - current through the coil
A - area of a coil


so,
(u1 / u2) = (N1 x I1 x A1) / (N2 x I2 x A2) ..... (i)

given,
N1 = N2. and I1 = I2

so, eqn (i) becomes:

u2 / u1 = A2 / A1 .......... (ii)

A1 = π R^2
A2 = a^2 , where a - side length of the square

length of the wire is fixed..
so,
total length of wire = 2πRN = 4aN
=> a = πR/2

=> A2 = (πR/2)^2

now,

u2 / u1 = A2/A1
$= {( \frac{\pi \: r}{2} )}^{2} \div (\pi \: {r}^{2} ) = \frac{\pi}{4}$

Answer 2

Answer:

if L is the length of the wire, then

L=N×2πR=N'×2πR/2

therefore N'=2N

Original magnetic moment, M=NIA=NI(πR^2) New magnetic moment,

M'=N'IA'=(2N)I πR^2/4

=1/2 NIπR^2

THEREFORE

M'/M =1/2 =1:2

THANK YOU