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Question

A circular coil of nturns and radius r carries a current i. It is unwound and rewound to make another coil of radius r2 current I remaining the same. calculate the ratio of the magnetic moments of the new coil and the original coil.


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Solution

Step 1: Given data

Originalturns=n

Originalradius=r

Originalcurrent=I

Newradius=r2

Newcurrent=I

NewTurns=2n

Step 2: To find

The ratio of the magnetic moments of the new coil and the original coil.

Step 3: Calculate the ratio

μ'μ=n'IA'nIA

Here,

μ and μ' is the magnetic moment.

n is the circular coil turns.

n' is the new circular coil turns.

I is the current.

A is the area of the coil.

A' is the area of the new coil.

μ'μ=2n×π4×r22n×I×π4×r2μ'μ=12

Hence, the ratio of the magnetic moments of the new coil and the original coil is 12.


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