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. `(mu_(0) i)/(2pi a) "tan" (pi)/(n)`
B. `(mu_(0) n i)/(2pi a) "tan" (pi)/(n)`
C. `(2)/(pi) ("ni")/(a) mu tan "" (pi)/(n)`
D. `("ni")/(2a) mu_(0) "tan" (pi)/(n)`

Answer

B

Explanation

`B_(1) = (mu_(0))/(4pi ) * (i)/( r) (sin theta + sin theta)`
`implies (mu_(0))/(2pi) (2i sin theta)/(r )`
`B_(1) = (mu_(0) i)/(2pi a) tan theta " "`[ as r = `a cos theta`]
`B_("net") = (n mu_(0) i)/(2pi a) "tan" (pi)/(n)`