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

Options

A. `(mu_0I)/(piR)(tan""pi/n)`
B. `(mu_0I)/(4piR)tan""pi/n`
C. `(mu_0I)/(2piR)(tan""pi/n)`
D. `(mu_0I)/(2piR)(cos""pi/n)`

Answer

C

Explanation

`B = (mu_0I)/(4pid)[(2sinpi)/n]`
But `cos"" pi/n=r/R" or "r = R cos""pi/n`
`:.B = (mu_0I)/(4piRcos""pi/n)[2sin""pi/n]`
`=(mu_0I)/(2piR)[tan""pi/n]`