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A coil carrying current 'I' has radius 'r' and number of turns 'n'. It is rewound so that radius of new coil is 'r4' and it carries current 'I'. The ratio of magnetic moment of new coil to that of original coil is

A
1
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B
12
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C
14
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D
18
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Solution

The correct option is C 14
Initially, the radius of the coil r1=r
Area of the coil initially A=πr2=πr2
Thus initial magnetic moment of the coil μ1=nIA=2πnIr2
Now the coil is rewound to form a new coil of radius r=r4 having n turns.
Length of the coil before and after its is rewounded remains the same.
n(2πr)=n(2π×r4)
n=4n
Area of the new coil A=π(r)2=πr216
Magnetic moment of new coil μ=nIA
μ=(4n)I×πr216=πnIr24
Thus ratio of magnetic moments μμ=πnr2/4πnr2
μμ=14

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