You place 4 charges of equal magnitude Q at the corners of a square of side length L, such that two of the charges are negative and two are...

Hello!

The electric potential of a point charge `q` at some another point is equal to  `1/(4pi epsilon_0) q/r,` where `r` is the distance from the point to the charge and `epsilon_0` is an absolute constant (the permittivity of vacuum). Note that `q` is a signed value.

Also, it is known that the electric potential of point charges is additive, i.e. the potential of a system of charges is equal to the sum of the point's potentials. So we need to compute `4` potentials and sum them.

The distance `r` is the same for all four charges, and it is `L/sqrt(2).` The magnitudes of the charges are also the same, `Q.` Thus the sum is

`1/(4pi epsilon_0) Q/r (1 + 1 - 1 - 1).`

`+1` is for positive charges, `-1` is for negative.

We see that the result is zero, and it doesn't depend even on the rearrangement of the charges.