a square with side length 2.0 cm has a charge of -1.0x10^-6C at every corner. What is the magnitude and direction of the electric force on each charge?

Question

What is the force on a fifth charge placed in the centre of this square?
Does the sign of the fifth charge affect the magnitude or direction of force on it?

Answer 1

Make the drawing:
charge #1 – at the left bottom corner,
charge #2 – at the left upper top cirner,
charge #3 – at the right top corner,
charge #4 – at the right bottom corner.
Forces actting on the Charge #4 are:
from #1 towards #4 F1=k•q1•q2/a²=k•q²/a² ,
from #3 towards #4 F3 = k•q1•q2/a²=k•q²/a² ,
from #2 towards #4 F2 = k•q1•q2/(a√2)²=k•q²/2•a² ,
F13=sqrt(F1² +F3²)= k•√2•q²/a².
F123= F13+F2 =k•√2•q²/a² + k•q²/2•a² =
= k•q²/ a•(√2+0.5) =9•10^9•10^-12•1.91/0.02 =0.86 N.
The equal net forces act on each charge.
The electric field strength is zero in the center of this square, therefore, the force acts on each charge in the center is zero as well.