Induced charges and their distribution

[arvindsharma]

Dear All,

I have some doubts in induced charges surface distribution.suppose their is a spherical shell and a negative charge is kept inside the shell(not at the center of shell) then induced charge distribution at inner surface of cavity is not uniform due to eccentric position of charge but the induced charge distribution at the outer surface of shell is uniform.can anyone explain me why induced charge distribution at outer surface is uniform?i have attached a file also to see the diagram.please go through it?

Thanks

Arvind

 

[Simon Bridge]

The outside charge, in your example, is not "induced" charge.
The negative point charge inside the shell has attracted positive free charges to the inner surface so that the electric field due to the inner charge is completely negated. The enclosed charge is completely screened and can have no effect on the world outside the inner surface of the shell.

If the conducting shell is not grounded, and it started out as neutral, then repositioning some positive charges on the inner surface has left negative free charges behind. Since the enclosed charge is totally screened off, these left-over charges feel only each other - they repel each other but must remain on the sphere. Thus they end up uniformly distributed across the outer surface.

 

[arvindsharma]

why outside charges are screened off?can anyone explain this in detail?i will be thankful.

 

[Simon Bridge]

The inside charges get screened because they are surrounded by an equal amount of (induced) opposite charge ... the interior charge and the induced charge make a net zero charge. Zero charge = zero force.

 

[sardar]

Dear Arvind,

Thank you for your question about induced charges and their distribution. The distribution of induced charges on a surface depends on the electric field created by the charge inside the spherical shell. When a negative charge is placed inside the shell, it creates an electric field that points towards the center of the shell. This electric field causes the positive charges in the shell to be attracted towards the inner surface, while the negative charges are repelled towards the outer surface. This results in a non-uniform distribution of induced charges on the inner surface of the shell, as shown in the attached diagram.

On the other hand, the outer surface of the shell is not affected by the electric field created by the charge inside. This is because the electric field lines originating from the charge inside are perpendicular to the outer surface, and therefore do not induce any charges on it. As a result, the induced charge distribution on the outer surface remains uniform.

I hope this explanation helps to clarify any doubts you may have about induced charges and their distribution. If you have any further questions, please do not hesitate to ask.

Sincerely,