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A wire carrying current i has the config...

A wire carrying current `i` has the configuration as shown in figure. Two semi-infinite straight sections, both tangent to the same circle, are connected by a circular arc of central angle theta, along the circumference of the circle, with all sections lying in the same plane. What must be for `B` to be zero at the centre of the circle?

A

`theta=1 rad`

B

`theta=2rad`

C

`theta=3rad`

D

None of the above

Text Solution

Verified by Experts

For `vecB` to be zero at the centre, sum of field due to the ring and that due to the semi-infinite straight section should be equal and opposite
i.e. `(mu_(0)i)/(2piR)-(mu_(0)i)/(2piR)((theta)/(2))=0`
`rArr (mu_(0)i)/(2piR)(1-(theta)/(2))=0`
`rArr theta=2` rad
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