A charged conducting ring rotating B field -- referece frames

[artis]

Admittedly I found similar threads here already but due to my rather lacking math skills I wanted to go through this myself.

As for the math side, I see various different equations with which this is treated can someone please provide the formulas for calculating B field from a rotating charged ring as measured from the center of the ring ,

I see the formula B= μ 0*I*r2/2(r2+z2)3/2 is used,
what is meant by z in it ?


1) Also on a theoretical side if a charged ring is spun around it's axis there is a B field in the non spinning frame, now if there is a stationary charged ring and next to it a disc that is now spinning then there is no B field in the stationary frame but there is a B field in the rotational frame of the spinning disc , correct?


2) Can a charged rotating ring if it is spun up and rotates within a perfect vacuum on magnetic bearings, does the magnetic field such a ring creates in the stationary frame of reference is non vanishing/permanent? As far as I can see there is no mechanism through which energy could be subtracted from this ring , apart from the charge on the ring draining away with time.


3)If one wanted to increase the charge on the ring one would need to have a "second plate" and good dielectric nearby but the "second plate" has to be stationary because if it were spinning at the same speed as the ring there would be no B field nor in the ring's frame nor in the stationary as the two opposite charge currents would cancel?

 

[anuttarasammyak]

Say the ring is on x-y plane with its center on Origin, you observe z axis. We can say (x, y, z) as coordinate of any space point. And
$$r=\sqrt{x^2+y^2}$$

 

[Dale]

I see the formula B= μ 0*I*r2/2(r2+z2)3/2 is used,
what is meant by z in it ?

You have been with us for more than two years. Please use LaTeX for formulas.