Answer to Question #133013 in Electricity and Magnetism for Afraid

Question

Four equal positive charges placed on corner on square. Find force on its centre

Answer 1

The force cannot exist itself, it is always acting on something. So let's suppose that we put some charge Q in the centre of the square and find force acting on this charge in centre.

1. Let's assume that Q<0, then the picture looks like on the drawing above.Coulomb forces that acting on -Q are $F_1, F_2, F_3, F_4$. Since all +q are equal, all forces $F_1, F_2, F_3, F_4$ have equal modulus, but different directions. Vector sum $F_1+F_2+F_3+F_4=0$ as can be seen from the drawing. However, note that +q will not be in equilibrium for any Q, because +q experience Coulomb force from interaction with other +q charges ($F_x$ and $F_y$ in the picture). So, all +q will be repulsing while -Q remain is centre.
2. Let's assume Q>0, then forces from the picture will change their direction to opposite. But the sum $F_1+F_2+F_3+F_4$ still remains zero. In this case for any value of +Q, system of +q will begin repulsing from central +Q while +Q remains at its place.

Answer: $F = \sum F_i=0$