What is the magnetic field at a distance R from a coil of radius r carrying current l ?

Options

A. `(mu_(0)nI)/(4r)`
B. `(mu_(0)nI)/(8r)`
C. `(mu_(0)nl)/(16r)`
D. `(mu_(0)nl)/(32x)`

Answer

C

Explanation

`B=(mu_(0))/(4pi)[(2pi nIr^(2))/((r^(2) +x^(2))^(3//2))] `
But `(x^(2) +r^(2))^(3//2) =[r^(2) +(sqrt3r)^(2)]^(3//2)`
`= (r^(2) + 3r^(2))^(3//2) =[(2r) ^(2)]^(3//2)=8r^(3)`
`therefore B =(mu_(0))/(4pi) [(2pi n I r^(2))/(8r^(3))]=(mu_(0)nI)/(16r)`