A point `P` lies on the axis of a flat coil carrying a current. The magnetic moment of the coil is `mu`. The distance of `P` from the coil is `d`, which is large compared to the radius of the coil. The magnetic field at `P` has magnitude

Options

A. `(mu_(0))/(2pi)((mu)/(d^(3)))`
B. `(mu_(0))/(4pi)((mu)/(d^(3)))`
C. `(mu_(0))/(2pi)((mu)/(d^(2)))`
D. `(mu_(0))/(4pi)((mu)/(d^(2)))`

Answer

A

Explanation

`B = (mu_(0)Nir^(2))/(2(r^(2) + d^(2))^(3//2)) = ((mu_(0) Nipi r^(2)))/(2pid^(3)(r^(2)//d^(2) + 1)^(3//2))`
`= (mu_(0)mu)/(2pi d^(3))`
Since `N i pi r^(2) = NiA = ,mu, r lt lt d, (r^(2))/(d^(2))` is negligible.