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A current i ampere flows in a circular a...

A current `i` ampere flows in a circular arc of wire whose radius is `R`, which subtend an angle `3pi//2` radian at its centre. The magnetic induction `B` at the centre is

A

`(mu_(0) i)/( R)`

B

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

C

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

D

`(3 mu_(0) i)/(8 R)`

Text Solution

Verified by Experts

The correct Answer is:
D
`B = (mu_(0))/(4pi) ((2pi - theta)i)/( R) = (mu_(0))/(4pi) ((2pi - (pi)/(2)) xx i)/( R) = (3mu_(0) i)/(8 R)`
Aliter : Magnetic field due to sector of coil-
`B = (mu_(0) )/(4pi) * (I theta)/( R)`
Here , `theta = (3 theta)/(2) , B = (mu_(0) I)/(4pi R) * (3pi)/(2) = (3mu_(0) I)/(8R)`
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