# Electric field at a point from a square surface

I'm trying to determine the electric field at a point P (located on the +Z axis) due to a square of side length [L] and centered at the x-y plane origin. The square has a constant surface density [s]. I'm thinking that I should go about splitting up the square into four smaller squares (one in each quadrant) and then calculate the field from each on the point P. Is this the correct way of solving this type of problem, or should I be splitting the big square up into infinitesimal strips and calculating the field that way?

-
Where are the comments from Ted and me? This Prawda-customs are disgusting. – Georg Mar 28 '11 at 9:29
The discussion was becoming a mess so I deleted it. Let's not get into that topic again. – David Z Mar 28 '11 at 12:12

Hint: The square is symmetric with respect to the transformation $x \to -x$. That means the x-component of the electric field must be equal minus itself i.e. it must be zero. Similarly for y. So the electric field only points up, and you can simply calculate the z-component for a strip and integrate in one dimension.

-

I don't see any advantage of cutting up the plate into four (you are basically asking the same question again: the field of an individual plate). The other way you suggest would work. Cut the square plate into tiny 1-D strips and integrate over.

-
Thanks for the reply. Any other tips on how I could go about doing that? – user2801 Mar 27 '11 at 21:12
Actually, it's even worse than asking the same question again: it's turning the original question into a harder one! In each of the new sub-problems, you'd have to figure out the field at an asymmetrically-located point. – Ted Bunn Mar 27 '11 at 21:15
@Zach -- It can be hard to answer questions like these at the right level, because we don't know what you do and don't understand. Can you give any kind of sketch of what you might try to do if you started down this road? What about if someone just asked you to figure out the electric field due to a line of charge? If you show us what you would do in that case, it might help. – Ted Bunn Mar 27 '11 at 21:19
@Zach: First figure out the field of a thin strip along a line joining its center and at an angle to it. You'll get this as a function of the distance from the center and the angle. Integrate this to get the final field. Only one independent quantity (angle or distance) remaining it would be a simple integral I guess. – Manu Mar 27 '11 at 21:21