Quick question about electric fields in capacitors.

[Ishida52134]

Homework Statement

At which location will the electric field between the two parallel plates of a charged capacitor be the
strongest in magnitude?
a. near the positive plate
b. near the negative plate
c. midway between the two plates at their ends
d. midway between the two plates nearest their center

Homework Equations

The Attempt at a Solution

The answer says that it's d. But isn't the electric field between two parallel plates constant? Since the electric field is the surface charge density / permitivity of free space?

 

[ehild]

The capacitor plates are finite and there is the edge effect: The electric field lines extend to the outer space near the edges, so the field strength close to the edges is slightly less than at the middle of the capacitor. The edge effect depends on the separation between the plates. If the plates are very far away from each other their electric field more and more resembles to that of two points charges.

ehild

 

[collinsmark]

Homework Statement

At which location will the electric field between the two parallel plates of a charged capacitor be the
strongest in magnitude?
a. near the positive plate
b. near the negative plate
c. midway between the two plates at their ends
d. midway between the two plates nearest their center

Homework Equations

The Attempt at a Solution

The answer says that it's d. But isn't the electric field between two parallel plates constant? Since the electric field is the surface charge density / permitivity of free space?

The answer you were given is wrong.

For an infinitely long, parallel plate capacitor (infinite area), you are correct that electric field is constant between the plates.

But for a finite area,even with the length of a plate, such that the length of a side $l$ is much , much greater (>>) than the distance between the plates, d, the electric field can be approximated as a constant. But in reality, if you draw a line from the midpoint of one plate to the other, the electric field is actually at a minimum at the center of that line, compared to the endpoints of that line. Again, the magnitude of E is approximately constant at all points of that line. But if you were pressed to specify (like you are here), the midpoint of the line has an ever so slightly less |E| than the endpoints. (Although it's true that the electric field's magnitude is greater on this line than it is on a line near the edge of the plates. I'm just saying that on this particular line, the electric field's strength is a minimum at the center of the line [midway between the positive and negative plate], not a maximum.)

'Time to raise heck, I guess.

[Edit: ehild beat me to the response (nice diagram too!)]