The magnetic field at the center of a current carrying loop of radius 0.1 m is `5sqrt( 5)` times that at a point along its axis. The distance of this point from the centre of the loop is

Options

A. 0.2 m
B. 0.05 m
C. 0.1 m
D. 0.25m

Answer

A

Explanation

Let us consider a point P at a distance x from the centre of loop, where magnetic field is given by `B_(0)=5sqrt5 B`, (`B_(0)` is the magnetic field at centre)
if current I is flowing through loop and radius of loop is R, then
`B=(mu_(0)IR^(2))/(2(x^(2)+R^(2))^(3 // 2))`
According to the question,
`5sqrt5(mu_(0)IR^(2))/(2(x^(2)+R^(2))^(3 // 2))=(mu_(0)I)/(2R)` `[ :' B_(0)=(mu_(0)I)/(2R)]`
`implies (sqrt5 R)^(3)=(x^(2)+R^(2))^(3 // 2) implies 5R^(2)=(x^(2)+R^(2))`
or `x^(2)=4R^(2)` or `x= +-2R`
Here, R = 0.1 m `implies` x = 0.2 m