Deriving potential energy by simulation method

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SUMMARY

The discussion focuses on deriving the equation for electrical potential due to a ring charge, specifically a charged coil or charged ring as described in electromagnetism literature. The electric potential is influenced by parameters such as the height (Z), diameter (R), and charge density (λ) of the ring. The derivation involves using the complete circle integral function and the Legendre function to express the potential at a point P. Participants emphasize the importance of determining the Cartesian coordinates of points on the ring to calculate the distance (l) for substitution into the potential formula.

PREREQUISITES
  • Understanding of electric potential and charge distributions
  • Familiarity with Legendre functions and their applications
  • Knowledge of complete circle integral functions
  • Basic proficiency in Cartesian coordinate systems
NEXT STEPS
  • Study the derivation of electric potential using Legendre functions
  • Explore complete circle integral functions in electromagnetism
  • Learn how to calculate Cartesian coordinates for points on a ring
  • Investigate numerical simulation methods for charge distributions
USEFUL FOR

Students and professionals in physics, electrical engineering, and applied mathematics who are interested in electromagnetic theory and the mathematical modeling of electric potentials.

aruwin
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The picture shows the potential due to ring charge.
Please show the full steps of deriving the equation of electrical potential. I don't know how to start at all.

NOTE:
The electric potential of the revolving symmetrical ring electric charge related to the axis z as depicted in the diagram 5.3, is also called a charged coil or a charged ring in the electromagnetism books, but most of the time, it gives an infinite series of equation that uses Legendre function. 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 diameter 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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Hi aruwin!

I may be a bit late, but if you're still interested...

What would the cartesian coordinates of a point on the ring be?

If you have that you can find the cartesian distance $l$ between the 2 points and substitute it in the formula that is given.
 

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