Calculate net electric force?

Question

four point charges +Q and -Q are arranged on the corners of a square of side L. what is the net electric force that these charges exert on a point charge q placed at the center of the square?

Answer 1

If the +Q charges are on opposite corners, on a diagonal, and the -Q charges are on the other diagonal, then the net force will zero, net electric force = 0.

The forces due two the two +Q charges are equal and opposite. They cancel. Similarly the forces due two the two -Q charges are equal and opposite. They also cancel.

If the +Q charges are on adjacent corners, and the -Q charges are on the other two adjacent corners, then the force will be in the direction from the center to the midpoint between the -Q charges.

As with your other question on net electric force,

http://answers.yahoo.com/question/index;...

we must calculate components in the x and y directions.

The distance from the center to a corner of the square is:

√(2L²)/2 =  Ã‚½L√(2).

The force between one +Q charge and the q charge is

1/(4πε))(Qq/(½L√(2))²) = 1/(4πε))(Qq/(½L²)) = 1/(2πε))(Qq/(L²)).

This force acts along a diagonal of the square. The magnitudes of the components parallel to the sides of the square are ½√(2) times the diagonal force = √(2)/(4πε))(Qq/(L²)).

The components of the forces due to the two +Q charges parallel to the line between them are in opposite directions and cancel out.

Similarly the components of the forces due to the two -Q charges parallel to the line between them are in opposite directions and cancel out.

The components of all four forces in the direction from the center to the midpoint between the -Q charges are all in the same direction; thus they add.

Net force = 4*√(2)/(4πε))(Qq/(L²)) = √(2)/(πε))(Qq/(L²)).

On your previous question the answer that you chose as best answer failed to take into account the components of forces that cancel. It is wrong.