A coil of n turns and radius R carries a current I it is unwound and rewound to make a new coil of radius `(R )/(2)` and the same current is passed through it what is the ratio of the magnetic moment of the new coil and the original coil ?

Options

A. `(1)/(6)`
B. `(1)/(8)`
C. `(1)/(4)`
D. `(1)/(2)`

Answer

C

Explanation

Let L be the length of the wire and n' be the number of turns in the new coil
Then `L=nxx2piR=n' (2pi.(R)/(2)) therefore n' =2n`
`therefore (M)/(M)=1/2`