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^(4))`
B. `(1)/(r ^(3))`
C. `(1)/(r^(2))`
D. `(1)/(r )`

Answer

B

Explanation

The maghnetic field at a point on the axis of a circular coil is given by
`B= (mu_(0))/(4pi) (2pi I R_(2))/((R^(2)+r^(2))^(3//2)`
But `r gt gt R.`
Hence `R^(2)` can be neglected in comparison with `r^(2).`
`therefore B = (mu_(0))/(4pi) [(2pi I R^(2))/(r^(3))]thereforeB prop (1)/(r^(3))`
Since all other quantities are kept constant.