Grounded conducting sphere with cavity (method of images)

Question

If I have a grounded conducting sphere with a cavity [radius $R$] that has a positive charge inside, using the image method to calculate the electric field I have to use an imaginary charge. My question is where is the charge located and why. The imaginary charge is placed inside the cavity or inside the conducting sphere but outside the cavity?
I know the imaginary charge cant be placed in the region where the electric field is being calculate. I know that because the sphere is grounded, the outer surface potencial is fixed [$V=0$] , but i dont understand what is happening inside. It is a conducting sphere so inside the electric field should be zero, but what happens if I place the charge inside the cavity or outside the cavity?

Joe Iddon · Answer

The method of images aims to set up charges so that the conductor lies on an equipotential surface. Two unequal point charges create a zero potential sphere that encompasses the smaller in magnitude of the two spheres.
It is hard to see in the picture below, but I made a simulation of equipotentials from point charges that shows the zero potential in green (place charges with left click, pan with right mouse, scroll to change charge magnitude).

This problem is completely discussed in more detail in the FLP here, going into how to calculate the positions of the point charges for a given zero sphere, I provide the picture below so you can see what will be discussed there.

Hopefully this answers you question of where you need to place the image charge - namely, outside the grounded sphere and with a negative charge.

Grounded conducting sphere with cavity (method of images)

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