---
title: "An electron and a proton are individually launched horizontally with the same initial speed \\(v_0\\) into a uniform electric field \\(\\vec{E}\\) between two horizontal parallel plates of length \\(L\\) and separation \\(d\\), as shown. Neither particle strikes either plate while traveling between the plates. How does the kinetic energy gained by the electron, \\(\\Delta K_e\\), compare to the kinetic energy gained by the proton, \\(\\Delta K_p\\), upon exiting the region between the plates, and why?"
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url: "https://nerd-notes.com/ubq/117506/"
date_modified: "2026-08-04T06:52:25+00:00"
---

# An electron and a proton are individually launched horizontally with the same initial speed \(v_0\) into a uniform electric field \(\vec{E}\) between two horizontal parallel plates of length \(L\) and separation \(d\), as shown. Neither particle strikes either plate while traveling between the plates. How does the kinetic energy gained by the electron, \(\Delta K_e\), compare to the kinetic energy gained by the proton, \(\Delta K_p\), upon exiting the region between the plates, and why?

An electron and a proton are individually launched horizontally with the same initial speed \(v_0\) into a uniform electric field \(\vec{E}\) between two horizontal parallel plates of length \(L\) and separation \(d\), as shown. Neither particle strikes either plate while traveling between the plates. How does the kinetic energy gained by the electron, \(\Delta K_e\), compare to the kinetic energy gained by the proton, \(\Delta K_p\), upon exiting the region between the plates, and why?

![Two horizontal parallel conducting plates of length \(L\) are separated vertically by a distance \(d\). Vertical electric field lines labeled \(\vec{E}\) point uniformly downward from the top plate to the bottom plate. At the vertical midpoint on the left entrance of the plates, a horizontal arrow labeled \(\vec{v}_0\) points to the right into the region between the plates. A dashed curved line indicates a parabolic path bending upward toward the top plate, exiting the right side of the plates without contacting either plate. Labels \(L\) and \(d\) indicate the horizontal length and vertical separation of the plates, respectively. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826344-Xea6l6.jpg)

- **A.** \(\Delta K_e = \Delta K_p\), because both particles carry a charge of magnitude \(e\) and traverse a region with the same potential difference \(\Delta V\).
- **B.** \(\Delta K_e = \Delta K_p\), because the electron's smaller mass produces a larger vertical acceleration that exactly cancels the mass dependence in the kinetic energy formula.
- **C.** \(\Delta K_e < \Delta K_p\), because the proton has greater mass and therefore experiences a greater electric force during its traversal through the plates.
- **D.** \(\Delta K_e > \Delta K_p\), because both particles experience the same magnitude of electric force for the same time interval, causing the electron to undergo a larger vertical displacement in the direction of the force.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117506/*