Question
A negative charge -Q is placed inside the cavity of a hollow metal solid. The outside of the solid is grounded.
Q: Is there any excess charge induced on the inner surface of the piece of metal?
A: Yes, +Q
Q: Is there any excess charge on the outer surface of the metal?
A: No
Q: Is there an electric field in the cavity?
A: Yes
I understand the first two. The +Q induced charge to match the -Q charge, and the outer part of the metal is neutralized. However, I don't understand the third. Wouldn't the electric field from the -Q and the field fromt the +Q induced charge cancel each other out?
Q: Is there any excess charge induced on the inner surface of the piece of metal?
A: Yes, +Q
Q: Is there any excess charge on the outer surface of the metal?
A: No
Q: Is there an electric field in the cavity?
A: Yes
I understand the first two. The +Q induced charge to match the -Q charge, and the outer part of the metal is neutralized. However, I don't understand the third. Wouldn't the electric field from the -Q and the field fromt the +Q induced charge cancel each other out?
Answers
Sean
Forget it... Inside the cavity of a charged metal object (such as a sphere or cylinder), there is no net field. The net field exists only on the outside.
That explains it.
That explains it.
Damon
Ah, not quite that simple.
There is no field inside a charged hollow ball that is only charged on the periphery.
However in this case there is a -Q at the center I and a +Q on the inner surface. There is an electric field between these two. You can apply Gauss Law around the charge at the center and get an E vector surrounding the charge at the center.
In fact that field continues outside the sphere with only a gap with No E field in the interior of the metal material of the shell itself. That is because in that metal shell material the Gauss surface surrounds the -Q at the center and the +Q on the interior surface of the metal, for a net charge inside of zero.
Outside the sphere, your Gauss surface encloses the -Q at the center, the + Q at the inner surface, and the -Q at the outer surface for a net charge of -Q enclosed for any point totally outside the sphere.
There is no field inside a charged hollow ball that is only charged on the periphery.
However in this case there is a -Q at the center I and a +Q on the inner surface. There is an electric field between these two. You can apply Gauss Law around the charge at the center and get an E vector surrounding the charge at the center.
In fact that field continues outside the sphere with only a gap with No E field in the interior of the metal material of the shell itself. That is because in that metal shell material the Gauss surface surrounds the -Q at the center and the +Q on the interior surface of the metal, for a net charge inside of zero.
Outside the sphere, your Gauss surface encloses the -Q at the center, the + Q at the inner surface, and the -Q at the outer surface for a net charge of -Q enclosed for any point totally outside the sphere.