A conducting wire carrying a current I is bent into the shape as shown. The net magnetic field at the centre O of the circular arc of radius R

Options

A. `(mu_(0)l)/(2R)((1+3pi)/(pi))`
B. `(mu_(0)l)/(4R)((1+3pi)/(pi))`
C. `(mu_(0)l)/(8R)((1+3pi)/(pi))`
D. `(mu_(0)l)/(8R)((2+3pi)/(pi))`

Answer

C

Explanation

The net magnetic field at the centre 'O' of the circualr arc is
`B_(0)=(mu_(0)l)/(4piR)+(3mu_(0)l)/(8R)-(mu_(0)l)/(8piR)`
`=(mu_(0)l)/(8piR)+(3mu_(0)l)/(8R)`
`B_(0)=((mu_(0)l)/(8R))((1+3pi)/(pi))`