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

Answer

D

Explanation

Magnetic field at a point on the axis of a loop is given by`B=(mu_(0))/(4pi)=(2pilR^(2))/(R^(2)+r^(2))^((3)//(2))`.
When rgt gt R,
`B=(mu_(0))/(4pi)(2piR^(2)l)/(r^(3))=(mu_(0))/(2pir^(3))`. Thus,B`oo1//r^(3)`.