I am having a lot of trouble trying to figure out how to find all the electric fields in and around a DC circuit. Although I have studied electric circuits for years, not much discussion has been given to these circuits' electric fields. And when I started to think about them a bit, I ran into a paradox that I am hoping someone on this forum can help resolve for me.
Now, I am aware of the relation between the electric field and voltage:
and of the point form of Ohm's Law:
but something has to give rise to E in the first place. This means that unpaired charges need to be present within the circuit. However, since
But you attach a capacitor across R3 in the circuit above and you let the circuit go to steady state, you would get the following charge distribution over the circuit:
!?! But shouldn't the charges on capacitor plates in circuits be equal and opposite? I seem to have a paradox here. Did I mislearn something somewhere, or what? Could someone offer me some more explanation here?
Now, I am aware of the relation between the electric field and voltage:
-grad V = E
and of the point form of Ohm's Law:
E = Jρ
but something has to give rise to E in the first place. This means that unpaired charges need to be present within the circuit. However, since
div J = 0
within a conductor at steady state, these charges must be present on the surfaces of the conductors. So, from my understanding, a simple DC circuit with a series connection of three resistors of equal resistance connected to a battery would look like this with its surface charges shown:
But you attach a capacitor across R3 in the circuit above and you let the circuit go to steady state, you would get the following charge distribution over the circuit:
!?! But shouldn't the charges on capacitor plates in circuits be equal and opposite? I seem to have a paradox here. Did I mislearn something somewhere, or what? Could someone offer me some more explanation here?