(where a charge particle is orbiting along the circumference).

Consider a charge +q rotating in anticlockwise sense in a circle of radius r with tangential speed v. Shown in Fig.

Thus, field at the centre, `B = (mu_0qv)/(4pir^2)`

`B = mu_0/(4pi) . (q2pirf)/r^2 = mu_0/(4pi)\ \ (2pifq)/r`

where f is the frequency of rotation.

or `B = (mu_0i)/(2r)` where `i = q/T = qf`, T is the period of rotation.

`text(Note :)` Behavior of moving charge along the circle is equivalent to a current carrying conductor.

As the charge is moving along the circle,

`B = mu_0/(4pi). (qvsin(pi/2))/(R^2 + x^2)` is the magnetic field at point P shown in Fig.(1e)

`B = mu_0/(4pi). (qv)/(R^2 + x^2) sin theta` When average is taken it behaves like current carrying ring.

Where `sin theta = R/(sqrt(R^2 + x^2))`

`B_(ax is) = 2 (mu_0qv)/(4pi(R^2 + x^2)) sin theta`

= `(mu_0 2piRfR)/(4pi(R^2 + x^2)^(3/2)) = mu_0/2. (qfR^2)/(R^2 +x^2)^(3/2)`

= `(mu_0iR^2)/(2(R^2 + x^2)^(3/2))`

Here, `B_(+) = (mu_0qvx)/(4pi(l^2 + x^2)^(3/2))`

`B_(n et) = (2mu_0qvx)/(4pi(l^2 + x^2))`

Note:
(1) Behavior of moving charge along circle is not equivalent to current carrying coil for instantaneous value of magnetic field on its axis.

(2) For average value of magnetic induction on the axis behaviour of moving charge is equivalent to the current carrying coil. Where `text(current = charge x frequency)`

{3) For symmetric charge distribution behaviour is equivalent to current carrying coil for both instantaneous and average value.