# What happens if we place an isolated charge on one plate of a parallel plate capacitor and how is the charge going to distribute?

I read somewhere that the charge redistributes equally is if 20c is place on one end, both of the other ends of the parallel plate capacitor has +10c and -10c. I want to know why and how such redistribution occurs. Also, if such redistribution occurs isn't conservation of charges violated?

• Even though your question is not a duplicate of this one Why do the charges on a parallel plate capacitor lie only on the inner surface?, I've explained this phenomenon in my answer to the same. – Guru Vishnu Mar 25 at 13:27
• Where are you getting the 20C to "place on one end"? – Bob D Mar 25 at 16:12

Suppose you have some series of parallel plates with charges $$Q_1$$, $$Q_2$$, up to $$Q_n$$, for example like this (I've drawn just four plates but this is going to apply to any number of plates):

Strictly speaking what I'm going to say only applies to infinitely large plates but in practice we just need the size of the plates to be large in comparison to their spacing. Anyhow, the charge on each plate distributes itself between the two faces of the plate in accordance with the rules:

1. the charges on the faces of a pair of plates is equal and opposite

2. the charges on the two outside faces are the same

3. if any plate is earthed the charges on the two outside faces are zero

If you're interested there is some discussion of why these rules apply in the question Why are the two outer charge densities on a system of parallel charged plates identical?

In your case you have just two plates, i.e. the two plates of your capacitor, and the charges are $$Q_1 = 20C$$ and $$Q_2 = 0$$. If we apply the rules above we find the charge distribution is:

Why would conservation of charge be violated in your example? A property of conductors is that, in electrostatic equilibrium there can be no field inside the conductor (for an ideal conductor, in real life there may be a small amount inside near the surface) and the conductor is at a constant potential. The excess change placed on a conductor is free to move about in the surface and any deviation from equilibrium will case changes to move until they find an equilibrium that satisfies the constraints previously mentioned.

What matters is that the total charge of all components in an isolated system remain fixed. The redistribution cannot change the total. In your example it would help if you provided some information on whether the caps are connected to each other or in isolation.