Question

A circular coil of N turns and diameter D carries current I. It is unwound and rewound to make another coil of diameter 2D, current I remaining the same. The ratio of magnetic moments of the original coil to the new coil is

• A. \(2:1\)
• B. \(4:1\)
• C. \(1:2\)
• D. \(1:4\)

Hint:

Wire length is fixed, so doubling the diameter halves the number of turns.

Answer 1

The Correct Option is C

Step 1: Use proportionality:
$M\propto N\cdot D^2$, and $N\propto\dfrac1D$ since the wire length is fixed.

Step 2: Combine:
So $M\propto\dfrac{D^2}{D}=D$. Doubling the diameter doubles the magnetic moment.

Step 3: Ratio:
$M_{old}:M_{new}=1:2$. Option C.

Final Answer:
Wire length fixes N inversely with D, so M is proportional to D, giving 1 : 2. \[ \boxed{\text{(C) }1:2} \]