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Question

The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is x. When both the current and radius is doubled the ratio will be

A
x8
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B
x4
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C
x2
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D
2x
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Solution

The correct option is A x8
The magnetic field at the centre of a current carrying loop is given by
B=μ04π(2πia)=μ0i2a
The magnetic moment at the centre of current carrying loop is given by M=i(πa2)
Thus, BM=μoi2a×1iπa2=μ02πa3=x (given)
When both the current and the radius are doubled, the ratio becomes
μ02π(2a)3=μ08(2πa3)=x8

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