Work done by electric field: W= q*E*d? Mistake

[stester77s]

My confusion comes from Khan Academy's video ()
At about 4:10 into the video.
To figure out the work done by a plate, he multiplies E*q*d to find the work done by the plate.

Here is my question:

Isn't the electric field constantly changing as you move across the electric field. Closer to the plate, isn't the value of E higher? And farther away from the plate, isn't the value of E smaller? As a result, it perhaps makes sense to say the force at any given point is equal to F=E*q, but it doesn't make sense to multiply by distance to get work, because the electric field (and consequently the force) will constantly be changing as you move closer or farther away from the plate.

Is my reasoning right? Please help clear my confusion. Thank you.

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[milski]

The field generated by a plate is uniform and does not depend on the distance from the plate. Of course, that's only true for an infinite plate but it is a very good estimation when you are not too close to the edges of the plate. In practice, you can treat E as constant whenever you are talking about the field between two plates.