# A charged conducting ring rotating B field -- referece frames

• artis
In summary, the conversation discusses the calculation of the B field from a rotating charged ring, the theoretical implications of a spinning disc and a stationary charged ring, and the possibility of increasing the charge on the ring with a stationary "second plate." The formula B= μ 0*I*r2/2(r2+z2)3/2 is used, where z represents the coordinate of any space point. The conversation also mentions the use of LaTeX for formulas and the need for a good dielectric nearby to increase the charge on the ring.
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?

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
$$r=\sqrt{x^2+y^2}$$

artis said:
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.

## 1. What is a charged conducting ring rotating in a B field?

A charged conducting ring rotating in a B field is a physical system in which a ring made of a conductive material is placed in a magnetic field and is rotating around its axis. The ring is also charged, meaning it has an excess or deficiency of electrons, which creates an electric field. As the ring rotates, it experiences both the magnetic and electric fields, resulting in interesting physical phenomena.

## 2. How does the rotation of the ring affect the B field?

The rotation of the ring affects the B field in two ways. Firstly, it causes the magnetic field lines to bend, creating a non-uniform magnetic field. Secondly, it induces an electric current in the ring, which in turn produces its own magnetic field that interacts with the external B field. This interaction can result in a variety of behaviors, such as precession or oscillation of the ring.

## 3. What are the different reference frames involved in this system?

There are two main reference frames involved in this system: the laboratory frame and the rotating frame. The laboratory frame is the stationary frame of reference in which the external B field is measured. The rotating frame is the frame of reference attached to the ring, in which the ring appears to be stationary. These two frames have different perspectives on the motion of the ring, which can lead to different interpretations of the physical phenomena.

## 4. How does the choice of reference frame affect the observations in this system?

The choice of reference frame can significantly affect the observations in this system. In the laboratory frame, the ring appears to be rotating, while in the rotating frame, the ring appears to be stationary. This can lead to different interpretations of the forces and fields acting on the ring, as well as the motion of the ring itself. It is important to carefully consider the reference frame when analyzing this system.

## 5. What are some practical applications of a charged conducting ring rotating in a B field?

There are several practical applications of this system, such as in electric motors and generators. In these devices, the rotation of a conductive ring in a magnetic field is used to convert electrical energy into mechanical energy or vice versa. This system is also studied in physics experiments to understand the effects of rotating reference frames and the interaction between magnetic and electric fields.

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