In the following figure a wire bent in the form of a regular polygon of `n` sides is inscribed in a circle of radius `a`. Net magnetic field at centre will be

Options

A. `B=(mu_(0)i)/(2pia)tan .(pi)/(n)`
B. `B=(mu_(0)ni)/(2pia)tan .(pi)/(n)`
C. `B=(2mu_(0)ni)/(pia)tan .(pi)/(n)`
D. `B=(mu_(0)ni)/(2a)tan .(pi)/(n)`

Answer

2

Explanation

Magnetic field at the centre due to one side
`B_(1)=(mu_(0)i)/(2pir)sin theta`, where `r=a cos theta`
`:. B_(1)=(mu_(0)i)/(2piacos theta)sin theta=(mu_(0)i)/(2pia)tan theta , :. B_(n e t)=nB_(1)`