If a thin wire of length L is given the shape of a regular polygon of n sides and current I flows through it, what will be the net magnetic field at the centre of the polygon if n is infinity?

Options

A. `(mu_(0)ni)/(2L)`
B. `(mu_(0)ni)/(2 pi L) `
C. `(mu_(0) pi i)/L`
D. `(mu_(0)n pi i)/L`

Answer

c

Explanation

If the number of sides is kept infinite , it means that we can assume the polygon to be a circular loop. Let r be the radius of the circular loop, then
`L = 2 pi r rArr r = L//2 pi `
Hence can write it as :
` B = (mu_(0)i)/(2 L/(2 pi)) = (mu_(0) pi i)/L `
Therefore, option (c ) is correct.