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 field induction at the center of polygon due to one side of the polygon is

Options

A. `"tan"(pi)/(n) tesla`
B. `(mu_(0)I)/(piR)["tan"(pi)/(n)] tesla`
C. `(mu_(0)I)/(2piR)["tan"(pi)/(n)] tesla`
D. `(mu_(0)I)/(2piR)["cos"(pi)/(n)] tesla`

Answer

C

Explanation

`B=(mu_(0)I)/(4pir) [2"sin"(pi)/(n)]`
But `"cos"(pi)/(n)=r/n`
or `r=R"cos"(pi)/(n)`

`:. B=(mu_(0)I)/(4piRcos(pi/n))[2"sin"(pi)/(n)]`
or `:. B=(mu_(0)I)/(2piR) ["tan"(pi)/(n)]`