# Why does each plate receive a charge exactly the same magnitude in parallel plate capacitor?

When a parallel plate capacitor is connected through a cell, each plate of the capacitor receives a charge with the same magnitude, but with the opposite sign. Is it because of the battery or the area of the plates?

• Conservation of electric charge ,if charges on one plate decreases , charges on the other plate must increase by equal amount.
– Paul
Jan 22, 2017 at 11:50

Suppose you have a simple circuit with a capacitor and a power supply:

You want to create a charge on the capacitor, so you turn on the PSU to add some extra electrons to the upper plate:

But the number of electrons in your circuit is constant. The power supply can't create or destroy electrons. All it can do is act like a pump to move electrons round the circuit. Specifically it can pump electrons from the bottom plate round the circuit to the top plate:

So for every electron that you add to the top plate you have to remove an electron from the bottom plate, and that means the negative charge on the top plate is necessarily always equal to the positive charge on the bottom plate.

• Sorry for reviving this but I had the same question. I have a question about your answer though. I suppose not PSU's are the same, but I'm thinking about a battery -- perhaps your answer is influenced by that. Don't the electrons on the bottom plate naturally want to go towards the battery since that's the anode? In other words, its not the push of the electron going towards the top plate, its the pull of the protons on the anode. Jun 25, 2019 at 20:15
• @TypicalHighschooler I deliberately left it vague as to what exactly the PSU is because it doesn't make any difference. In the case of a battery a chemical reaction inside the battery consumes electrons on one side and emits electrons on the other so one side has a net negative charge and the other a net positive charge. The electrons in the circuit are simultaneously pushed away by the negative charge on the anode and pulled towards the positive charge on the cathode. Jun 26, 2019 at 4:56
• So then my question is this: aren't the electrons in the bottom plate naturally attracted to the cathode since there is positive charge there? For example, consider a case where you only connect the bottom plate to the cathode; you don't connect the top plate to the anode. Then the electrons in the bottom plate and the wire will spread out since there is the positive terminal of the battery attracting them. In this case, after you connect the top plate to the anode, there won't be equal charge on both plates. Jun 26, 2019 at 15:31

The battery creates a potential difference between its terminals. Because, in a steady state situation, the total voltage through a closed circuit is zero, this will create, when the capacitor is charged, the same voltage over this component. Then, if the charges on the capacitor plates wouldn't be equal in magnitude (!), the electric field outside (and inside as well) the capacitor would not be zero. However, in steady state the electric field inside a (perfect) conductor, the wires in this case, is always zero.