How Is Electrical Potential Derived from a Ring Charge?

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Discussion Overview

The discussion revolves around deriving the electrical potential from a ring charge, focusing on the complexities introduced by variable lengths in the calculations. Participants seek to clarify the steps involved in this derivation, particularly in relation to a diagram depicting the potential due to a ring charge.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses confusion about deriving the equation for electrical potential due to a ring charge, indicating that the length is a variable.
  • Another participant suggests that the problem may stem from the variable nature of "l," which is the distance from a part of the ring charge to point P, and proposes expressing "l" in terms of r and θ.
  • A participant notes that the diagram does not depict a revolving system, prompting a check on the assumptions made in the problem.
  • One participant claims to have solved the problem but does not provide the resolution in the thread.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the derivation steps, and multiple viewpoints regarding the approach to the problem remain. The discussion reflects uncertainty and varying levels of understanding among participants.

Contextual Notes

There are limitations regarding the assumptions about the system being analyzed, particularly concerning the depiction of the ring charge and the nature of the variable "l." The discussion does not resolve these aspects.

MissP.25_5
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Hi.
I have no idea how to do this. It's complicated because the length here is a variable. I posted the same question before but there was a little mistake so I am reposting this again.

The picture below shows the potential due to ring charge.
Please show the full steps of deriving the equation of electrical potential shown in the picture. I have no idea how to start.

NOTE:
The electric potential of the revolving symmetrical ring electric charge related to the axis z as depicted in the diagram 5.3. It is commonplace to use complete circle integral function in the charge simulation method. If the position (height) of ring electric charge is Z, the radius is R, and the charge density is λ, the electric potential of the point P will be as represented in the next equation.

In the equation, l is the distance between the part of the ring charge dθ and P.
 

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MissP.25_5 said:
Hi.
I have no idea how to do this. It's complicated because the length here is a variable. I posted the same question before but there was a little mistake so I am reposting this again.

The picture below shows the potential due to ring charge.
Please show the full steps of deriving the equation of electrical potential shown in the picture. I have no idea how to start.
I can give you a hint where to start, but I am not allowed to provide full steps like you ask.

The electric potential of the revolving symmetrical ring electric charge...
... the picture does not show a revolving system - please check.

... related to the axis z as depicted in the diagram 5.3. It is commonplace to use complete circle integral function in the charge simulation method. If the position (height) of ring electric charge is Z, the radius is R, and the charge density is λ, the electric potential of the point P will be as represented in the next equation.

In the equation, l is the distance between the part of the ring charge dθ and P.
So how would you normally go about finding the potential due to a distribution of charge?

You problem seem to be the "l" is not fixed?
That is not a problem if you express l in terms of r and θ
 
Simon Bridge said:
I can give you a hint where to start, but I am not allowed to provide full steps like you ask.

... the picture does not show a revolving system - please check.


So how would you normally go about finding the potential due to a distribution of charge?

You problem seem to be the "l" is not fixed?
That is not a problem if you express l in terms of r and θ

It's ok, I have solved this problem!
 
Excellent - perhaps you can help out someone in a similar fix by posting the resolution?
 

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