A loop carrying current I has the shape of a regular polygon of n sides. If R is the distance from the centre to any vertex, then the magnitude of the magnetic induction vector `vec(B)` at the centre of the loop is –

Options

A. `n"" (mu_(0) I)/(2pi R) "tan" (pi)/(n)`
B. `n"" (mu_(0) I)/(2pi R) "tan" (2pi)/(n)`
C. `(mu_(0) I)/(2R)`
D. `(mu_(0)I)/(pi R) "tan" (pi)/(n)`

Answer

A

Explanation

`B_(0) = (mu_(0))/(4pi ) (I)/(R cos"" (pi)/(n)) [ sin"" (pi)/(n) + sin "" (pi)/(n)]`
`B_(0) = (mu_(0))/(2pi) (I)/( R) "tan" (pi)/(n)`
`B = nB_(0) implies B = n ((mu_(0))/(2pi) (I)/( R) "tan" (pi)/(n))`