Brownout & I have both shown that Id = Ic as have at least 2 of the lectures that were posted.
One showed that Ic = 1.2 e^(-t/RC) & Id = 1.2 e^(-t/RC). So what numbers do you need to play with?
Hi again,
We know that numerically they are equal, but that doesnt prove that they are the same. I can have two eggs in one carton and two eggs in another carton, but the two pairs are not the same eggs even though we count them as being the same. That's the difference between numerical equality and theoretical equality. If the two currents were exactly the same right down to the particle we wouldnt have to call one by a different name.
The numbers i am talking about are to map out atomically what would happen if we say that electrons go into one side of the capacitor and flow through the capacitor and come out the other side, then how do we say that a large quantity of those electrons stayed on the plate (ie accumulated)? For example, we know that the ampere is 1 coulomb per second, and we know the charge of 1 electron. We also know the chemical makeup of materials used for conductors and materials used for dielectrics (and BTW we also know that a vacuum does not contain any atoms to speak of). From there, we can work out, from the physical size and structure of the system , exactly where these electrons come from and where they go and just what the limits of a given system would be. If the limits of the system do not allow a certain theory to work out numerically, then the theory fails. It's that simple.
The problem that we face right away though is even simpler. We know that charge accumulates on one plate and depletes on another plate. We also know that when charge accumulates it does not travel any longer, but 'bunches up' in a group. Thus one plate is covered with excess charge and the other plate is missing a lot of charge. But in the dynamic case, we dont have this right away, but it gradually works up to that point as time goes on. So the action then, and this should be very easy to picture, is we have two bodies separated by a short distance in space, and one body is losing charge and the other body is accumulating charge, and the charge that leaves one plate is the same as the charge that enters the other plate. In a perfectly symmetrical system, went we have one electron leave one plate we have one electron enter the other plate. Thus, the current on both sides of the capacitor measures the same value. Now if we look at this like two storage containers instead of two plates, one container looses a brick and the other container gains a brick. Now, if we say that the bricks somehow flow through, then the first container (say on the left) can not hold that brick but must pass it through the space between the plates. If this happened, the plate on the right would again have the same charge as before because it both lost a charge and gained a charge, and we know that means it would still have no net charge. For the plate on the left, it gained an electron but then spit it back out, so the net charge there would be zero also.
This is one reason why charge can not pass through the capacitor, because it would not allow charge to deplete on one side and build up on the other side.
Does this make sense to you or no?
Lets look at another quick example. If we take a unit of charge and place it into a metal container with a vacuum inside, what happens?
We can measure the state of the charge of the system from the OUTSIDE of the container, even though the charge inside does not touch the metal inside the container. The metal of the container takes on the value of the charge, even though the charge does not touch the container. How can this happen? Is the charge moving from the center to the inside of the metal somehow? Well we covered that case because we make sure the charge doesnt touch the inside of the container, so we dont have to ask that question.
But we still detect the charge from outside the container, and the reason for this is because of the field inside the container. We dont have to have the charge move physically to touch the inside, we just do nothing really and the field does it all. We could then remove the charge and it would still maintain the same value.
The field acts over long distances too, not just over microscopic scales.