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Question

A current i is flowing in a specific wire. It is turned into a circular coil of one turn. Then it is turned to make a coil of two turns and smaller radius. Now the magnetic induction at the centre for same current will be

A
half of its previous value
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B
one fourth of its previous value
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C
four times of its previous value
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D
zero
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Solution

The correct option is D four times of its previous value
Let the radii be r1 and r2 respectively.
Since there are two turns of radius r2, r1=2r2
Magnetic field B at the center of the coil of radius r1 B1=μoi2r1=μoi4r2
Magnetic field B at the center of the coil of radius r2 B2=2×μoi2r2
B2B1=2×μoi2r2μoi4r2=4

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