[Maple] Calculating the potential produced by a charge

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SUMMARY

The forum discussion centers on the discrepancies in calculating the electric potential produced by a charge outside a conducting grounded sphere using different computational tools: Maple, Mathematica, and PocketCas. The charge, set at 1 Coulomb and positioned at <0.2 m, 0.2 m, 0.3 m>, yields inconsistent results, with Maple outputting approximately 3.18, Mathematica providing 0.0000114441, and PocketCas correctly returning zero at the sphere's surface. The example references Jackson's "Classical Electrodynamics," specifically Section 2.2, Eqs 2.1 to 2.5, which outlines the theoretical framework for this calculation.

PREREQUISITES
  • Familiarity with Maple 2023 for computational physics.
  • Understanding of electric potential and image charge method.
  • Knowledge of Mathematica 13 for numerical analysis.
  • Basic concepts of electrostatics as outlined in Jackson's "Classical Electrodynamics."
NEXT STEPS
  • Review Jackson's "Classical Electrodynamics," Section 2.2 for theoretical background.
  • Learn how to implement the image charge method in Maple 2023.
  • Compare numerical results from Mathematica 13 and PocketCas for consistency.
  • Explore troubleshooting techniques for discrepancies in computational physics outputs.
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This discussion is beneficial for physics students, computational physicists, and anyone interested in numerical methods for electrostatics, particularly those using Maple or Mathematica for simulations.

Mauro Silva
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I have been using Maple for sometime as its document interface feels nicer and more friendly than mathematica's . I have never been able to plot arrows in Mathematica or use indices efficiently. I am more of a curious self teaching physics person. But I just found something interesting when calculating the potential produced by a charge placed outside of a conducting grounded sphere. This example is fully worked out by Jackson - Section 2.2 - Eqs 2.1 to 2.5.
In my numerical example the charge q= 1 Coulomb is placed at the coordinates <0.2 m, 0.2 m, 0.3 m> . The sphere has radius 0.1 m.
It happens that on the sphere, say at <0 m, 0 m, 0.1 m>, the potential should be zero but Maple evaluates it to 10/Pi ~ 3.18 and Mathematica evaluates it to 0.0000114441. On the other hand PocketCas for IOS 10 is giving me exactly zero!
Has anyone seen this kind of problem? Would I making any dumb mistakes ?
 
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Unless you show the code you are using, there is not much anyone can do to help.
 
In the example, the potential is understood to be 0 at the sphere's surface. Are you trying to calculate the potential of the charge & image charge system (without the conductor), and use that result to represent the potential of the charge & conductor system for points outside of the conductor?
 

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