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)/(2 R)`
C. `(2mu_(0) i)/(R )`
D. `(3 mu_(0) i)/(8 R)`

Answer

D

Explanation

`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)`