If we double the radius of the coil keeping the current through it unchanged, the magnetic field on its axis at very very far away points

Options

A. double
B. three times
C. four times
D. one fourth

Answer

B

Explanation

If `rgt gtR`
`B=(mu_(0)NiR^(2))/(2(R^(2)+r^(2))^(3//2))=(mu_(0)NiR^(2))/(2r^(3)(R^(2)//r^(2)+1)^(3//2))=(mu_(0)NiR^(2))/(2r^(3))`
`B prop R^(2) implies B prop("radius of coil")^(2)`