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

Options

A. `mu_(0)I//R`
B. `mu_(0)I//2R`
C. `2mu_(0)I//R`
D. `3mu_(0)I//8R`

Answer

C

Explanation

For a loop, magnetic induction at centre,
`B=(mu_(0))/(4pi)xx(2piI)/R`
When loop subtends angle `theta` at centre, then
`B=(mu_(0))/(4pi)xx(thetaI)/R`
In the given problem, `theta=3pi//2`
`:. B=(mu_(0))/(4pi)xx(3pi)/2xx 1/R=(3mu_(0)I)/(8R)`