Find the electrostatic potential above loop of charge Q?

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Homework Help Overview

The problem involves determining the electrostatic potential at a point above a circular wire with a uniform charge distribution. The charge Q is distributed along a thin circular wire located in the z = 0 plane, and the potential is to be evaluated at the point (0, 0, D).

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to identify relevant components affecting the potential, questioning the need for specific equations and the relevance of the angle between the point and the loop. Some participants clarify that electrostatic potential is a scalar quantity and suggest breaking the wire into infinitesimal charge segments. Others provide a formula for the potential due to a continuous charge distribution and discuss the distance from the wire to the evaluation point.

Discussion Status

The discussion has progressed with participants providing clarifications on the nature of electrostatic potential and suggesting approaches to set up the integral for calculation. The original poster indicates they have resolved their confusion, suggesting a productive direction has been achieved.

Contextual Notes

Participants are navigating the complexities of integrating over a continuous charge distribution and ensuring the correct application of the potential formula. There may be assumptions about the uniformity of the charge distribution and the geometry of the setup that are being explored.

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Homework Statement


An electric charge Q is uniformly distributed along a thin circular wire situated in the z = 0 plane at x2 + y2 = R2 . Determine the electrostatic potential at the point (0, 0, D).

Homework Equations

The Attempt at a Solution


I figured the only components that mattered would be the one perpendicular to the wire since the parallel components would cancel with the other side of the wire. But I'm not sure what equation to use, or how to approach this. I also found tan of the angle between the point and the loop is R/D, not sure if I need that?

Thanks in advance.
 
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Keep in mind that electrostatic potential is not a vector quantity. So, there are no components. You'll need to know the formula for the potential of a point charge. Break the circular ring into infinitesimal bits of charge, each bit acts like a point charge.
 
So potential due to a continuous distribution of charge : V= 1/(4πε0)∫dq/r

Where r is the distance of the wire to the point at which you are trying to find the potential. In this case, D.
So since the wire has a radius R. The r=√(R2+D). This is because all points along the ring are at the same distance from the point at (0,0,D).

So then plugging this into the first equation, do you notice anything interesting? Perhaps a constant you can factor out leaving you with an easy integral.
 
Thanks for the help, figured it out now. :)
 

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