Immediately After Time T=0, What Happens To The Charge On The Capacitor Plates?

When a capacitor is fully charged, there is a certain amount of charge on each of the capacitor plates. As described in the above article, when the capacitor is disconnected from both of its source terminals, the charges on each plate stay where they are.

However, as this article will explain, that is not the case when the capacitor is disconnected at time t=0, when the circuit is first formed. At that moment, one of the plates loses all its charge, and it happens very quickly!

This article will discuss in detail exactly what happens to the charge on each plate immediately after time t=0. This information can be useful in understanding some basic circuit dynamics.

The article also discusses some interesting applications of capacitors that are disconnected at time t=0. These applications can be useful in understanding how some circuits work and what types of effects they have.

The electric field between the plates remains unchanged

As explained above, at time t=0, the electric field between the capacitor plates remains unchanged. This is because the distance between the plates does not change when the capacitor discharges.

The fact that the capacitor discharges means that the voltage across its plates changes, but not that its electric field changes. The electric field between its plates stays constant at all times unless a phenomenon comes about to change it.

A phenomenon such as this one occurs when there is a break in the circuit between the capacitor and whatever force it discharges to (ground). In this case, there would be no more force pulling electrons off of the positively charged plate, so it would have no more charge. As a result, there would be no more force opposing the electric field between the plates and therefore it would disappear.

The capacitor is an imperfect device

A capacitor is an electrical device that stores charge on two separate plates. The capacitor is analogous to a bottle, where you can pour water in, but it’s difficult to pour it out.

Like a bottle, the amount of charge a capacitor can store is limited by its size. You can’t put as much water in a small bottle as in a large one.

The major limitation of capacitors is that charges can only slowly diffuse through the separating dielectric material. This means that when you apply voltage to the plates, charges do not immediately flow from one plate to another and out of the capacitor. Instead, they build up on one plate before flowing to the other plate and out of the capacitor. This limiting property is called internal resistance.

Because of these limitations, when we apply time-dependent voltage across the capacitor, some charge may not flow out immediately.

Charge is not lost immediately after t=0

While it may seem like charge would be immediately redistributed after the time t=0, this is not the case. Charge is not lost immediately after t=0.

As explained by PhysLink, charge can neither be created nor destroyed, only redistributed. This makes sense, as our universe is made up of matter and atoms are what contain charge.

Since charge cannot be destroyed, the capacitor plates will hold their charges until they are discharged by some outside force. This force can either be a different electric field or time passing.

The more you understand about how time passes, the weirder this seems. Time passing does not actually cause anything to change in terms of charge distribution. Things just keep acting as they are because of time passing, but things do not change because of it.

Energy is stored in the capacitor

Once the circuit is complete, the capacitor stores energy in the electric field between its plates. The capacitor holds a steady voltage, so as the current drops, so does the voltage across the capacitor.

As current drops to zero, so does the voltage across the capacitor. Since there is no current flowing, there is no more energy being stored in the capacitor. It then returns to its neutral state with equal positive and negative charges on its plates.

The more capacitance a capacitor has, the more energy it can store. The length and width of the plates do not affect how much energy it can store; only how many electrons it can hold does. This makes capacitors with different sizes interchangeable for most applications.

The voltage across the capacitor remains the same

As the capacitor discharges through the resistor, it delivers energy to the circuit.

While the capacitor is connected to the circuit, its voltage remains the same as before time t=0. The energy in the capacitor is stored voltage, so as it discharges, it delivers voltage to the circuit.

As it discharges, more current flows through the circuit, so at time t=0, there is a moment when there is no voltage across the capacitor. This moment is called short circuit: there is no opposition to current flow.

After time t=0, there continues to be a difference in charge between the plates of the capacitor. The amount of charge on each plate does not change due to this experiment. The only thing that changes is how much current flows through the resistor and back into the capacitor.

The current through the capacitor remains the same

Once the voltage on the capacitor is equal to the voltage on the plate, there is no more charge to transfer. The current through the capacitor will stop.

Since the current through the capacitor remains constant, it follows that the voltage across the capacitor must also remain constant.

By Newton’s law of motion, a body will maintain its state of motion unless an external force acts upon it. In this case, since there is no external force acting upon it, the charged particle will continue in its state of motion.

Since there is no longer any potential difference between its plates, however, it will not continue to move toward one plate or the other; it will simply stand still between them. This is what we mean when we say that “the particle stands still at time t=0.

Breakdown of the dielectric occurs behind time t=0

Dielectric breakdown occurs when the electric field strength across a dielectric material reaches the point of failure.

Dielectric breakdown can occur in both insulating and semiconductor materials, however, in this article we will be focusing on dielectric breakdown in insulators. Insulators are non-conducting materials that separate electrical fields.

In this article, we will be discussing the consequences of breakdown on capacitors and how to avoid device failure due to breakdown. Capacitors rely on dielectrics to separate electric fields, thus making them vulnerable to breakdown.

When a capacitor is charged, its plates store an amount of energy proportional to the voltage across its plates and the number of plates (area). When a dielectric breaks down, this energy storage capability decreases.

Voltage across a capacitor also depends on the separation between its plates (dieletric thickness) which breaks down with double layers or corona discharge which increases surface charge density. This reduces the voltage across the capacitor.

Question 1: Immediately after the time $t=0$, the capacitor plates retain their charge.
Answer 1: Yes, it is impossible for all charges to move instantly, as this would violate Maxwell’s equations. At most, there might be a small change in potential due to screening effects.

As was mentioned in the article, after the switch is flipped, there is a period of time where the capacitor plates retain their charge.

There is a slight change in potential between the two plates, which results in a very slight current flow. This continues until enough potential difference builds up across the capacitor plates, at which point there is a sudden drop in voltage across the plate with the lower voltage and higher resistance.

This results in a sudden flow of current.

Question 2: What happens to the electric field immediately after time $t=0$?
Answer 2: The electric field inside the capacitor remains unchanged. Outside of the capacitor, there is no electric field. Therefore, outside of the capacitor no charge will be affected by this electric field.

As previously stated, outside of the capacitor there is no external electric field due to this configuration. Any surrounding charges will remain where they are unless attracted or repulsed by something else.
More information about Electric Fields can be found here.