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Electrostatics of 4 charges arranged in a square 
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#1
Mar2811, 08:29 AM

P: 4

1. The problem statement, all variables and given/known data
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? 2. Relevant equations Coulomb's Law F=[tex]\frac{k Q1 Q2}{r^{2}}[/tex] 3. 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. 


#2
Mar2811, 10:28 AM

P: 68

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. 


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