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Magnetic Field Due to a Circular Arc at the Centre

Current i i...

Question

Current $i$ is flowing in a circular coil of radius $a$ , then magnetic induction at centre is $B$ . If the current is doubled then magnetic induction will be

A

2 B

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B

B

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C

4 B

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D

2 \sqrt{2}

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Solution

The correct option is D $2 B$
The magnetic induction in a circular coil of radius a, carrying current i, is
$B = \frac{μ_{0} i}{2 a}$
If the current is doubled,
$B^{'} = \frac{μ_{0} (2 i)}{2 a}$
$B^{'} = 2 \frac{μ_{0} i}{2 a}$ or
$B^{'} = 2 B$

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