I\'m trying to determine the electric field at a point P (located on the +Z axis
ID: 2284917 • Letter: I
Question
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?
Explanation / Answer
The square is symmetric with respect to the transformation x??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.