A current I flows through a thin wire shaped as regular polygon of n sides which can be inscribed in a circle of radius R. The magnetic fidl induction at the center of polygon due to one side of the polygon is

Options

A. `(mu_0I)/(piR) (tanpi/n)`
B. `(mu_0I)/(4piR) tanpi/n`
C. `(mu_0I)/(2piR) (tanpi/n)`
D. `(mu_0I)/(2piR) (cospi/n)`

Answer

C

Explanation

(c) `B=(mu_0I)/(4pir)[2sin pi/n]`

But `cos pi/n=r/R or r=Rcos pi/n`
`:. B=(mu_0I)/(4piR cos pi/n)[2sin pi/n]=(mu_0I)/(2pir)[tan pi/n]`