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Magnetic Field Due to a Circular Arc at the Centre

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Question

A current carrying coil is bent sharply so as to convert it into a double loop both carrying current in the same direction. If $B$ be the initial magnetic field at the centre, then what will be the final concentric magnetic field?

A

2 B

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B

4 B

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C

8 B

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D

Zero

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Solution

The correct option is A $4 B$
Radius of the double loop, $r = \frac{R}{2}$
where, $R$ is the radius of single loop $B$ (centre)
$= \frac{μ_{0}}{4 π} \cdot \frac{2 π I}{R}$ .
So, magnetic field due to each coil is double of that due to single coil.
and total magnetic field
$= 2 B + 2 B = 4 B$ .

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