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An are of a circle of a radius R subten...

An are of a circle of a radius R subtends an angle `(pi)/(2)` at the centre .it carries a current l. The magnetic field at the centre will be

A

`(mu_(0)I)/(2R)`

B

`(mu_(0)I)/(8R)`

C

`(mu_(0)I)/(4R)`

D

`(mu_(0)I)/(5R)`

Text Solution

Verified by Experts

The correct Answer is:
B
Magnetic field at the center of a circular are of radius R, carries current I and making an angle`phi` at the centre is given by
`B=(mu_(0)Iphi)/(4piR)`
In the given problem `phi=(pi)/(2)`
`phi=(pi)/(2)`
`:. B=(mu_(0)I(pi"/"2))/(4piR)=(mu_(0)I)/(8R)`
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Knowledge Check

  • An arc of a circle of raduis R subtends an angle (pi)/2 at the centre. It carriers a current i . The magnetic field at the centre will be

    A
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    B
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    C
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    `(mu_(0)l)/(2 sqrt2 pi a)`
    B
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    D
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