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. `3/8 (mu_(0)i)/®`
B. `8/3 (mu_(0)i)/(r )`
C. `3/4 (mu_(0)i)/(r )`
D. `5/8 (mu_(0)i)/(r )`

Answer

A

Explanation

For a circular arc, subtending an angle `theta` at its centre,
`B=(mu_(0))/(4pi) [(theta .i)/(r)]`
For a circle, `theta= 2pi. ` In this case, `theta =(3pi)/(2)`
`therefore B = (mu_(0))/(4pi ) [(3pi)/(2)xx (i)/(r)]therefore B =3/8. (mu_(0)i)/(r)`