A coil carrying a current 'I' has radius 'r' and number of turns 'n' it is rewound so that radius of the new coil is `(r )/(4)` and it carries current `I' The ratio of the magnetic moment of the new coil to that of the original coil is

Options

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

Answer

C

Explanation

`M_(1) = nI (pi r^(2))`
now, n (`2pi r) = n. (2pi "" ( r)/(4)) implies n. = 4n`
`M_(2) = 4nl [ pi ((r^2)/(4))^(2)] = (M_(1))/(4)`