# Outside the capacitor plates E is zero how potenital the same

## Main Question or Discussion Point

hi,

We see theoretical discussion of Electric field inside the charged capacitor is confined in the space between the plates and E.d = potential difference between plates. Considering the battery terminal(let us say positive terminal), wire and left plate or top plate, being in the same potential, let us try calculating the potential on the outside surface of top plate. Since the electric field is zero, the work done in carrying a positive test charge from infinity to the outside surface of the top plate, will be zero. But the potential cannot be zero since battery terminal, wire and the plate are at the same potential. What is wrong here?

Bob

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jtbell
Mentor
Since the electric field is zero, the work done in carrying a positive test charge from infinity to the outside surface of the top plate, will be zero.
Correct, with a caveat that I'll discuss at the end.

But the potential cannot be zero since battery terminal, wire and the plate are at the same potential. What is wrong here?
Nothing. The fact that the electric field is zero in some region does not imply that the potential is also zero in that region. It implies that the difference in potential between any two points in the region is zero, i.e. that all points in the region have the same potential. In this case, that potential would equal the potential of the positive terminal of the battery.

Caveat: I'm talking about the idealized parallel-plate capacitor whose plates extend to infinity. This is not actually physically possible, of course. Besides the fact that it would take a lot of material to build the capaciitor, where would we put the battery and the return wire? Also, we'd have a region of zero potential extending to infinity on one side of the capacitor, and a region of constant nonzero potential extending to infinity on the other side, which isn't physically possible.

For a real, finite-sized capacitor connected in a circuit with a battery, the electric field is not zero outside the capacitor, and the potential falls off to zero as you go to infinity in any direction. Nevertheless, in a region close to one of the plates of the capacitor, in which the capacitor "looks like" it's practically infinite, the potential is almost constant on either side of the capacitor, and the electric field is almost zero.