Question about an image charge problem

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To solve the image charge problem for a grounded conducting plane and sphere, one must place image charges symmetrically opposite to the actual charge with respect to the boundary. For a grounded conducting plane, the image charge is equal in magnitude but opposite in sign, positioned at the same distance from the plane. For a grounded conducting sphere, the configuration involves a more complex relationship, typically requiring the use of a point charge and a specific distance based on the sphere's radius. The discussion highlights the confusion regarding whether the problem is in 2D or 3D, emphasizing the need for clarity in boundary conditions. Understanding these configurations is crucial for accurately applying the method of image charges in electrostatics.
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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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