A circular coil of radius `R` carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance `r` from the centre of the coil, such that `r gtgt R`, varies as

Options

A. `(1)/(r)`
B. `(1)/(r^(3))`
C. `(1)/(r^(2))`
D. `(1)/(r^(3//2))`

Answer

B

Explanation

The magnetic field due to a cicular coil of radius `R` at a point on the axis of the coil located at a distance `r` from the centre of the coil,
`B = (mu_(0))/(4pi) (2pi I R^(2))/((R^(2) + r^(2))^(3//2))`
Given `r gtgt R` then we have, after neglecting `R`,
`B = (mu_(0))/(4pi) (2pi i R^(2))/(r^(3))`
Also area `= pi R^(2)`