Four electrons move from point A to point B in a uniform electric field as shown below.Rank the electrons in diagrams I through IV by the changes in potential energy from most positive to most negative when travelling from A to B.

Question

Quizplus · Accepted Answer

The change in potential energy of an electron is given by EPE = qΔV, where q is the charge of the electron and ΔV is the change in voltage or electric potential. Since all four electrons have the same charge, the change in potential energy will depend only on the change in voltage they experience.

From A to B, the voltage decreases, meaning the electric potential becomes more negative. Electrons will move from higher potential (more positive) to lower potential (more negative) to decrease their potential energy.

In diagram II, the electron moves perpendicular to the electric field and does not experience any change in potential energy. Hence, it has the least change in potential energy.

In diagrams I and IV, the electrons move parallel to the field lines in the same direction as the field. In this case, the change in potential energy will be negative because the electrons are moving from higher potential to lower potential. However, the electric field is stronger near the bottom plate, so the voltage decreases more rapidly near that plate. This means that electrons in diagram I will experience a greater change in potential energy than those in diagram IV.

In diagram III, the electron moves parallel to the field lines but in the opposite direction of the field. In this case, the change in potential energy will be positive because the electron is moving from lower potential to higher potential. Moreover, the electric field is weaker near the upper plate, so the voltage decreases less rapidly near that plate. Therefore, the electron in diagram III will experience the greatest change in potential energy.

Thus, the ranking of electrons from most positive to most negative change in potential energy is II > I = IV > III, which corresponds to choice D.

Four Electrons Move from Point a to Point B in a Uniform