A current i is flowing in a straight conductor of length L. The magnetic induction at a point distant `L/4` from its centre will be-

Options

A. `(4mu_(0)i)/(sqrt(5)piL)`
B. `(mu_(0)i)/(2piL)`
C. `(mu_(0)i)/(sqrt(2)L)`
D. zero

Answer

A

Explanation

`B=(mu_(0)i)/(4piR) (sin theta_(1)+sin theta_(2))`
`sin theta_(2)=(L//2)/(sqrt((L//2)^(2)+(L//2)^(2)))=1/(2(sqrt(1//4+1//16)))=4/(2sqrt(5))`
`rArr B=(mu_(0)i)/(4piR)((2xx4)/(2sqrt(5))) B=(4mu_(0)i)/(sqrt(5)piR)`