Question

Four identical positive charges q are placed at the four vertices of a square of side a. Determine the electric field:
A) at the center of the square
B) at the midpoint of one of its sides

Answer 1

A - ROTFL - everything is equal and opposite to everything else

B - now we have a problem
the two on the same side cancel each other but the two on the opposite charge try to push away at 90 degrees to the side

distance from each = sqrt (a^2 + .25 a^2) = a sqrt (5/4)

component perpendicular to side
= [2 k q /(5 a^2 /4)] sin theta
where sin theta = 1/[ sqrt5/4]

= 2 k q/[ a^2 (5/4)^1.5 ]