Charge induced on capacitor plates

[Hijaz Aslam]

Homework Statement

Three conducting capacitor plates are kept horizontally, above each other with a gap 'd'. If a charge $+1\mu C$ is kept on the middle plate what is the charge on the plates?

Homework Equations

(This question is theoretical)

The Attempt at a Solution

My textbook gave the charge of the plates (starting from the upper face of the topmost plate) : $+0.5\mu C$, $-0.5\mu C$,$+0.5\mu C$,$+0.5\mu C$,$-0.5\mu C$,$+0.5\mu C$.

My question is: when we have opposite charges on the opposite faces of a plate (here the topmost and the lowermost, due to induction), won't there be an electric field created inside the capacitor plate (due to the opposite charges on the opposite faces, starting from positive face to negative)? And as it is a conductor is this allowed?

//Sorry that I couldn't upload a picture

 

[TSny]

If you consider the top plate, it will have positive charge on one face and negative charge on the other face. These charges on the top plate would produce a nonzero electric field inside the conducting material of the top plate. However, what is the net electric field inside the material of this top plate due to all of the charge in the system (including the charges on the faces of the other two plates)?

 

[Hijaz Aslam]

Oh yes, the mechanism of the equilibrium is like this: The middle plate has a net positive charge, this creates an electric field in the conductor, so to counter this electric field the top plate rearranges its charges as said above. Am I right?

 

[TSny]

Yes, that's right.

 

[HalfLostAndSearching]

of the capacitor plates
Yes, there will be an electric field created inside the capacitor plate due to the opposite charges on the opposite faces. This is allowed because the capacitor plates are conductors, which means they have free electrons that can move in response to an applied electric field. The electric field inside the plate will cause the free electrons to redistribute, resulting in a net negative charge on the inner surface of the plate and a net positive charge on the outer surface. This redistribution of charges will continue until the electric field inside the plate is equal to the electric field outside the plate, resulting in a stable equilibrium. Therefore, the charges on the plates as given in the textbook are correct and in accordance with the principles of electrostatics.