Book Online Demo

Check Your IQ

Try Test

Courses

A circular loop of radius $R$ carrying a current $I$ is unwound and rewound into a loop of half the radius. The current in the loop remains the same. The ratio of magnetic moments of the new loop to that of the old loop is

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

1 : 2

1 : 4

1 : 3

2 : 1

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The ratio of magnetic moments of the new loop to that of the old loop is

1 : 2

.
Let Area of the coil initially,

A = π R^{2}

Initial magnetic moment

μ = NIA = NI (π R^{2})

Length of the coil initially

L = N (2 πR)

Radius of new coil formed

R^{'} = \frac{R}{2}

and the number of turns in new coil be

N

.
But the length of the new coil

(L')

formed must be equal to that of original coil

L' = L

∴ N^{'} = 2 N

Thus, area of new coil

A' = \frac{{πR}^{2}}{4}

Magnetic moment of new coil

μ' = N' IA'

\Rightarrow μ' = 2 NI \times \frac{π R^{2}}{4}

\Rightarrow μ' = \frac{NIπ R^{2}}{2}

Hence, the ratio between the magnetic moments is given by

\Rightarrow \frac{μ}{μ'} = \frac{1}{2}

Hence, the ratio of magnetic moments of new loop to that of old loop is

1 : 2

Watch 3-min video & get full concept clarity