Question

A circular coil of wire of $n$ turns has a radius $r$ and carries a current $i$. Its magnetic dipole moment is $M$. Now the coil is unwound and again rewound into a circular coil of half the initial radius and the same current is passed through it, then the dipole moment of this new coil is :

• A. $\frac{M}{2}$
• B. $\frac{M}{4}$
• C. $M$
• D. $2M$

Answer 1

The correct option is A $\frac{M}{2}$

The length of remains same $N_1\pi \ast r=N_2\pi \ast r/2$

$N_2=2n$

$M=NAI=nI\pi \ast r^2$

$M_2=N_{2}I\ast \pi \ast (r/2{)}^2=2n\ast I\pi \ast (r^2/4)$

$\frac{M_2}{M}=\frac{1}{2}$

$M_2=\frac{M}{2}$