How Does Coulomb's Law Apply to a Charge in the Center of a Square?

[radenm]

Homework Statement

four charges aranged on the corners of a square. a fifth charge is located in the middle of the square. what is the net charge on that charge?
givens: two charges -5uC are placed at opposite corners of the square, two charges 2uC are placed at opposite corners of the square, and the fifth charge is -1uC placed at the middle of the square

Homework Equations

F=K(q1*q2)/r^2

The Attempt at a Solution

i do not know if i can find a distance to use the coulombs law equation.
the answer that i want to say is that there is no force exerted on the fifth charge because the charges at the corners opposite from each other are equal thus giving no exerted force.

 

[LowlyPion]

Are you asked for the net charge on the middle charge that you list as a given already? Or the net force perhaps?

I note that since the charges on opposite corners are equal and in opposite directions and you are equidistant from them ...

 

[radenm]

it is asking for the net force on the middle charge, and i keep thinking that the net force will be 0 because the charges on opposite corners are of equal direction and magnitude.
i just don't know if there is some law or rule that i am unaware of that will put any force on that middle charge

 

[LowlyPion]

it is asking for the net force on the middle charge, and i keep thinking that the net force will be 0 because the charges on opposite corners are of equal direction and magnitude.
i just don't know if there is some law or rule that i am unaware of that will put any force on that middle charge

Well there is Coulomb's Law that serves to show that very thing. Remember that force is a vector, and the statement of Coulomb's Law includes the vector in the direction between the charges.

 

[radenm]

dont i need the distance for each side to figure out the force generated from each charge?

 

[LowlyPion]

dont i need the distance for each side to figure out the force generated from each charge?

Write out the equations and see what cancels out.

 

[radenm]

thank you very much, your clarification was very helpful! :)