What is the magnetic field at the centre of arc in the figure below?

Options

A. `(mu_(0))/(4pi)*(2i)/(r )[sqrt(2)+pi]`
B. `(mu_(0))/(4pi)*(2i)/(r )[sqrt(2)+(pi)/(4)]`
C. `(mu_(0))/(4pi)*(i)/(r )[sqrt(2)+pi]`
D. `(mu_(0))/(4pi)*(i)/(r )[sqrt(2)+(pi)/(4)]`

Answer

b

Explanation

Distance of straight path from O
`=(r )/(sqrt(2))`
Hence , `B=B_(1)+B_(2)`
`(mu_(0))/(4pi)*(2i)/(r )+(mu_(0))/(4pi)(2pii)/(r )((1)/(4))`
`=(mu_(0))/(4pi)*(2i)/(r )[sqrt(2)+(pi)/(4)]`