Equilibrium of Four Point Charges in a Square: Calculating Charge Q

[badd99]

Four identical point charges of q = 8.37 nC are at the four corners of a square with a side length of 11.2 cm as shown in the figure. (had to make it but same thing since I can't copy it)

q q

Q

q q

Edit: doesn't come out right when I post so imagen a square little q's on corners and big Q in the center.

What charge Q should be placed at the center of the square to keep the other four charges in equilibrium?

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I have no idea how to even start. There are so many vectors here I can't figure out where to even beginning making things equal electrical pull/push

 

[Tomer]

Well, start by specifically writing the forces acting by 3 charges on the fourth one. You should know similar signs reject each other and different signs attract. By calculating the sum of the forces, see what force it is that will balance it.

The same charge will work for all other charges because of the symmetry of the problem.

 

[Doc Al]

Start by picking one of the four charges (the upper right, for instance) and figure out the force that each of the other three exert on it. Once you find the net force from those three, you can figure out what Q would have to be to counter that force.

(Edit: Looks like Tomer beat me to it.)

 

[Spinnor]

You should know you need to put a negative charge at the center to balance the forces. Look at the forces on any corner charge. There will be four forces that act on it, the three forces from the other corner charges and the force from the charge at the middle.

Rotate the square so that you only need to consider forces in the x direction. See the attached sketch. Hope that helps.