A circular coil of radius r, and carrying a current I has a magnetic dipole moment M. What is its new dipole moment, if the radius of the coil is doubled and the current passing through the coil is halved?

Options

A. `M_(2)=M_(1)`
B. `M_(2)=M_(1)/2`
C. `M_(2)=2 M_(1)`
D. `M_(2)=3M_(1)`

Answer

C

Explanation

The magnetic moment (M) of the current carrying coil is `M=n IA=nI (pi r^(2))`
It is given that `I_(2)=I_(1)/2, r_(2)=2r_(1)` and `n=1`
`:. M_(2)/M_(1)=(I_(1)/(2I_(1)))xxpi/pi ((4r_(1)^(2))/r_(1)^(2))=1/2xx4=2`
`:. M_(2)=2 M_(1)`