Consider a straight piece of length x of a wire carrying a current i. Let P be a point on the perpendicular bisector of the piece, situated at a distance d from its middle point. Show that for d>>x, the magnetic field at P varies as (`1/d^2) whereas for d << x, it varies as 1/d.

Explanation

Since O is the mid point of `MN = l`.
So , `B =(mu_oi)/(4pi)`. `(2l)/sqrtl^(2) + 4d^(2)`.
If `dgtgtx, thus B = (mu_oi)/(4pid)`. `(2l)/(2d)`.
i.e. `B prop (1)/(d)` .