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Question

# A current passing through a circular coil of two turns produces a magnetic field B as its centre. The coil is then rewound so as to have four turns and the same current is passed through it. The magnetic field at its centre now is:

A
2B
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B
B2
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C
B4
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D
4B
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Solution

## The correct option is C 4BLet the radius of the initial circular coil be rThus length of the coil L=2(2πr)Now the coil is rewound so as to have 4 turns such that the length of the coil is same.∴ L=4(2πr′)=2(2πr) ⟹r′=r2Magnetic field at the centre of the coil Bc=μo4πir(2πn) where n is the number of turns of the coil.For 1st case : n=2 ⟹B=μo4πir(2π×2)=μoir .........(1)For 2nd case : n′=4 r′=r2⟹B′=μo4πir2(2π×4)=4μoir From (1), we get B′=4B

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