Four point charges and an electron: electric field, potential, force and potential energy in eV.

Given four point charges and an electron, we compute electric field, potential, force and potential energy in eV when an electron is placed at the center of the square.

00:00 Given four identical point charges on the corners of a square, we compute the electric field at the center of the square. The electric field vanishes by symmetry because the field contributions cancel pairwise at this point (the field contributions add vectorially to zero).

01:19 Next, we compute the electric potential at the center of the charge configuration. To get the electric potential, we add together the contributions to electric potential from each of the four point charges. All four of these contributions are positive, and they add to the total electric potential at the center. We apply the formula V=kq/r for the electric potential near a point charge and we multiply by four to obtain the potential at the center.

03:11 We compute the electric force on an electron placed at the center of the charge configuration. Because the electric field is zero at the center, we immediately see that the force must vanish as well, since F=qE. In other words the electron is pulled toward each of the four corners of the square with equal magnitude, so the vector sum of all the forces is zero.

03:35 We compute the electric potential energy contribution of an electron placed at the center of the charge distribution. We express the potential energy in electron-volts. We show the long way to do this: start with the point-charge potential energy formula PE=kQq/r, and compute the potential energy of the interaction between the electron and one of the point charges, then multiply the answer by four to account for the interactions with the other point charges. Then we convert the potential energy to electron-volts using the standard conversion factor. Alternatively, we could have used a shortcut: we have an electron sitting at a known electric potential, and this means the energy in electron-volts will have the same numerical value as the potential we already computed earlier in the problem!