Question: Q. 2. A circular coil of $N$ turns and radius $R$ carries a current $I$. It is unwound and rewound to make another coil of radius $R / 2$, current $I$ remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil. A [O.D. 2012]
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Solution:
Ans. We have :
$$ \begin{aligned} N_{1} \cdot 2 \pi R & =N_{2} \cdot 2 \pi(R / 2) \ N_{2} & =2 N_{1} \end{aligned} $$
Magnetic moment of a coil, $m=N A I$
For the coil of radius ’ $R$ ‘,
$$ m_{1}=N I A_{1}=N I \pi R^{2} $$
For the coil of radius $R / 2$,
$$ \begin{aligned} & m_{2}=N_{2} I A_{2}=2 N I \pi R^{2} / 4=N I \pi R^{2} / 2 \quad 1 / 2 \ & \Rightarrow \quad m_{1}: m_{2}=1: 2 \quad 1 / 2 \end{aligned} $$
[CBSE Marking Scheme 2012]
