Question about an image charge problem

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SUMMARY

The discussion focuses on the setup of image charges to satisfy boundary conditions for grounded conducting planes and spheres. The user seeks clarification on how to deduce the correct configuration of image charges in both 2D and 3D scenarios. It is confirmed that image charges should be placed at the opposite side of the boundaries, and the user expresses familiarity with configurations for both grounded conducting planes and spheres, as well as hemispherical bumps attached to planes.

PREREQUISITES
  • Understanding of electrostatics and image charge theory
  • Familiarity with grounded conducting boundaries
  • Knowledge of 2D and 3D coordinate systems
  • Basic principles of charge distribution and potential theory
NEXT STEPS
  • Study the method of image charges for grounded conducting planes
  • Explore image charge configurations for grounded conducting spheres
  • Investigate the application of image charges in 2D versus 3D scenarios
  • Learn about the effects of hemispherical bumps on image charge setups
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Students and professionals in physics, particularly those studying electrostatics, as well as educators looking for effective methods to teach image charge problems.

Jefferson Yun
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Homework Statement


.
image charge problem.jpg

With this problem, how should I set image charges so as to satisfy the same boundary condition?
And if possible, could you let me know how can that image charge configuration be deduced?
Thanks for reading.

Homework Equations

The Attempt at a Solution


Well, I first put images charges just at the opposite side of the planar and spherical boundary. But I don't know what to do next.
 
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I guess the boundary is like this in 3D, right? :
Capture.PNG


Do you know how to set up image charge for grounded conducting plane and for grounded conducting sphere?
 
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arpon said:
I guess the boundary is like this in 3D, right? :
View attachment 107796
arpon said:
I guess the boundary is like this in 3D, right? :
View attachment 107796

Do you know how to set up image charge for grounded conducting plane and for grounded conducting sphere?
Do you know how to set up image charge for grounded conducting plane and for grounded conducting sphere?
No, actually it was 2d. But that situation is confusing as well. Could you let me know how should I set image charges in that situation, if possible?
And I know how to set the image charges for a ground conducting sphere or a plane. I know how to for a hemispherical bump attached on a plane as well.
 
Untitled.png

If you know how to set mirror charges for grounded conducting plane and sphere, this picture is enough hint for you.
 

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