Question

Can you explain me how exactly does the image method works in a conducto,r with spheric cavity(radius R) with a charge inside ,when is grounded and when it isnt?

If the conductor is grounded it means there there is a flow charges from inside to the outside of the conductor without changing the potencial of the conductor's surface. The main property of a conductor is that the electric field inside is zero. If I have a charge inside of the cavity I need to place an imaginary charge inside or outside of the cavity? In a simpler scenario with a grounded sphere, If I want to calculate the electric field outside of the sphere I place an imaginary charge inside of the sphere, so they cancel each other, and in this case i want the exact same thing , the field outside the conductor, right? But if the charges cancel, and the conductor is grounded where is the electric field?

In the case the conductor isnt grounded I really dont get it...

Answer 1

Image charge should not be in the region where source charge is present. For example, in the grounded infinite plane problem the image charge is in the other region where there is no source charge. So if the source charge is inside the cavity, image charge will be outside the cavity.

If you place a charge inside the sphere, image charge should be outside the sphere at a distance such that these two charges creates an equipotential spherical surface with zero potential( grounded sphere). So the electric field is to be calculated using this image and source charges without considering the grounded conductor because these two situations are identical.

If the conductor is not grounded, we have to choose the image charge such that the souce and image charge creates an spherical equipotential surface with that much of potential as given on the actual conductor. Then the two situations will be identical and we can calculate the electric field using source and image charges without considering the actual spherical conductor.