A coil of ' n ' turns and radius ' R ' carries a current 'I'. It is unwound and rewound to make a new coil of radius 3 R and the same current is passed through it. The

Question

A coil of ' n ' turns and radius ' R ' carries a current 'I'. It is unwound and rewound to make a new coil of radius 3 R ​ and the same current is passed through it. The ratio of the magnetic moment of the new coil to that of the original coil is

TestHub · Accepted Answer

The length of the wire remains constant when the coil is unwound and rewound.

$L = n \times 2 π R = n^{'} \times 2 π R^{'}$

Given $R^{'} = \frac{R}{3}$

$n \times 2 π R = n^{'} \times 2 π (\frac{R}{3})$

$n^{'} = 3 n$

The magnetic moment of the original coil is $M_{1} = n I π R^{2}$

The magnetic moment of the new coil is $M_{2} = n^{'} I π (R^{'})^{2}$

$M_{2} = (3 n) I π (\frac{R}{3})^{2} = \frac{1}{3} n I π R^{2}$

The ratio of the magnetic moment of the new coil to that of the original coil is

$\frac{M _{2}}{M _{1}} = \frac{\frac{1}{3} n I π R ^{2}}{n I π R ^{2}} = \frac{1}{3}$

Answer: $\frac{1}{3}$

Physics - Magnetism Question with Solution | TestHub

Options:

Doubts & Discussion