A point charge `q` moves with a non-relativestic velocity v = const. Applying the theorem for the circulation of the vector `H` around the dotted circle shown in Fig, `H` at the point `A` as a function of a radius vector `r` and velocity `v` of the charge.

Explanation

We use Maxwell's equations in the form,
`oint vec(B). D vec(r) = epsilon_(0) mu_(0) (del)/(del t) int vec(E). D vec(S)`,
when the condiuction current vanishes at the site.
We know that,
`int vec(E) d vec(S) = (q)/(4pi epsilon_(0)) int d Omega = (q)/(4pi epsilon_(0)) 2pi (1 - cos theta)`,
where, `2pi (1 - cos theta)` is the solid angle, formed by the disc like surfac, at the charge.
Thus, `oint vec(B).d vec(r) = 2pi a B = (1)/(2) mu_(0) q sin theta.theta`
On the other hand `x = a cot theta`
differening and using `(dx)/(dt) = -v`
`v = a cosec^(2) theta theta`
Thus, `B = (mu_(0) q v r sin theta)/(4pi r^(3))`
This can be written as, `vec(B) = (mu_(0) q(vec(v) xx vec(r)))/(4pi r^(3))`
and `vec(H) = (q)/(4pi) (vec(v) xx vec(r))/(r^(3))` (The sense has to be checked independently.)