Electric field between charged parallel plates?

[johny_doe]

We were told that the electric field between two oppositely charged parallel plates was uniform in any region between them: like
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but the teacher didn't really explain why: it makes sense that they'd always be in the same direction, but how would you prove that it's uniform throughout?

 

[gnome]

"...the electric field between two oppositely charged parallel plates was uniform in any region between them..."

...IF the plates are infinite.

Otherwise, it's very nearly uniform near the center, and less so the nearer you get to the edges.

Think of it in terms of the symmetry of the arrangement.

 

[johny_doe]

the symmetry bit makes sense... but why would the electic field be the same at the point centre (between them) as at a point very very close to one of them?

 

[MathStudent]

Analyze how charges near the end of the plate affect the electric field along a line perpendicular to the center. ( Referring to your picture above) At a point close to the positve plate, most of the E is contributed from the center of the plate and points straight down. The charges on the ends contribute mostly horizontal components which cancel due to symmetry. As the points move farther away, The E from the center of the plate decreases since the distance increases, but the ends contribute more to the vertical component because the angle of the line between the charge and the point changes. This makes up for the increase in distance from the center.

If your having trouble seeing this, then draw a line that bisects the plate, and plot corresponding E vectors at points along the line from a point charge at each end of the plate.

 

[johny_doe]

could i plot the field along some horizontal/vertical line by making some kind of general equation for the e-field caused by some point along the two plates (as a function of x-coordinate of point along plate, x,y)
then taking the integral of f(x,y,a) from a=-5..5 (assuming those are the boundaries of the plates)
and then graphing that for random values of x and y?

sorry if that didn't make sense