Electric Potential: V=-ED for Capacitors?

[collegeconfid]

Homework Statement

Why is the change in the electric potential between two capacitors V=ED ?

Homework Equations

V=-ED

The Attempt at a Solution

Isn't the change in electric potential equal to the negative of the product of the electric field and displacement?
So, why is it that for a capacitor the change in potential is not V=-ED ?

Thanks for any help.

 

[willem2]

You mean the change in potential between the 2 plates of a capacitor?

Actually the equation $\Delta V = -E \cdot D$ is satisfied

$E \cdot D$ is the dot product of the vectors of the electric field and the displacement.
It's +|E||D| if they are in the same direction and -|E||D| if they are in opposite directions.

(|E| is the magniture of the electric field |D| is the magnitude of the displacement)

In a capacitor, the electric field points from the positive plate to the negative, so from the higher potential to the lower. If you move in the direction of the electric field, then both E and D have
the same direction, but you're moving to a lower potential, which is as it should because $-E \cdot D$ is negative