Electrostatics of 4 charges arranged in a square

[fizziksr0cks]

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 q_o placed at the center of the square? (b) What are the magnitude and the direction of the force on the test charge q_o 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 q_o 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 q_o is placed on. If q_o 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 q_o ?

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.

 

[Berko]

What was your result for part a? Yes, always assume the test charge is positive. You should have gotten a very convenient result.

As for b) (and a)), remember that Coulomb's Law is a vector law. You need to take into account directions and not just magnitudes.