A coil of ' $n$ ' turns and radius ' $R$ ' carries a current 'I'. It is unwound and rewound to make a new coil of radius $\frac{R}{3}$ and the same current is passed through it. The ratio of the magnetic moment of the new coil to that of the original coil is

Question

Aicharya · Accepted Answer

Let the initial magnetic moment be $\mu_1=n_1 I A_1$ $=\mathrm{n}_1 \mathrm{I} \pi \mathrm{R}_1{ }^2$
And, the final magnetic moment $\mu_2=\mathrm{n}_2 \mathrm{I} \pi \mathrm{R}_2^2$ Given, $\mathrm{R}_1=\mathrm{R}, \mathrm{R}_2=\frac{\mathrm{R}}{3}$, $\Rightarrow \mathrm{n}_2=3 \mathrm{n}_1$ $\therefore \quad \frac{\mu_2}{\mu_1}=\frac{\mathrm{n}_2}{\mathrm{n}_1}\left(\frac{\mathrm{R}_2}{\mathrm{R}_1}\right)^2=3 \times\left(\frac{1}{3}\right)^2=\frac{1}{3}$

A coil of ' $n$ ' turns and radius ' $R$ ' carries a current 'I'. It is unwound and rewound to make a new…

Solution