If the distance x of a point on the axis of a circular loop carrying current I is much larger than the radius of the loop, show that the magnetic field at that points is proportional to `(1)/(x^(3))`.

Explanation

The magnetic field `B=(mu_(0)I)/(2)*(r^(2))/((r^(2)+*x^(2))^(2//3))`
`(r^(2)+x^(2))^((3)/(2))=[ x^(2)((r^(2))/(x^(2))+1)]^((3)/(2))~~[x^(2)(0+1)]^((3)/(2))=x^(3)`
`:.B prop (1)/(x^(3))`