# Electrostatics of 4 charges arranged in a square

## Homework Statement

Four charges are arranged on the corners of a square whose edge length is a. Two positive charges +Q are placed on diagonally opposite corners, and two negative charges -Q are placed on the other corners. (a) What is the force on a test charge qo placed at the center of the square? (b) What are the magnitude and the direction of the force on the test charge qo if it is placed at the midpoint of one of the edges?

## Homework Equations

Coulomb's Law-

F=$$\frac{k |Q1| |Q2|}{r2}$$

## The Attempt at a Solution

(a)
I drew myself a picture of all the forces in a square with 1 set of diagonals positive and the other set negative. "a" represents the side length.

I'm not really sure where to go with this. I tried Coulomb's law for repulsive forces on qo by Q1, etc. and then did the same for attractive forces. The test charge is positive correct?

(b) I think I have this part figured out. Because all sides have one positive charge and one negative charge it doesn't matter which midpoint qo is placed on. If qo is positive then it will be repelled by +Q and attracted by -Q in a linear way. The only thing I'm unsure of is the two remaining charges not on the same line. Do they have any effect on the force of qo ?

Instead of just posting an answer is it possible for you to show your thoughts/steps? I'd like to know the thought process for this type of problem instead of just the answer. Thanks for your help.