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Question

The magnetic induction due to circular current-carrying conductor of radius a, at its centre is Bc. The magnetic induction on its axis at a distance a from its centre is Ba. The value of Bc:Ba will be :

A
2:2
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B
1:22
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C
22:1
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D
2:2
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Solution

The correct option is B 22:1
The magnetic induction due to circular current-carrying conductor of radius a, at its centre is
Bc=μ0I2a (1)

The magnetic field on the axis of a current-carrying circular coil of radius r at a distance d from its center is given by
B=μ0Ir22(d2+r2)32

Here, r=d=a, hence

Ba=μ0Ia22(a2+a2)32

or, Ba=μ0Ia22(2a2)32

or, Ba=μ0I42a (2)

Therefore, from (1) and (2),

BcBa=22


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