A proton and an electron are projected from the origin along the positive x-direction in a region where the electric potential increases along the x-axis. What happens to their speeds?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → The speed of the proton decreases and that of the electron increases
The electric field points in the direction in which the potential decreases. Here the potential increases along +x, so \( \vec{E} \) points along −x. A positive charge is pushed along \( \vec{E} \) and a negative charge opposite to it.
Option (1) The speeds of both decrease — Incorrect. The proton and the electron carry opposite charges, so the field pushes them in opposite directions. The electron is pushed along +x, the direction of its motion, so it speeds up.
Option (2) The speeds of both increase — Incorrect. The proton is pushed along −x, against its motion along +x, so it slows down.
Option (3) The speed of the proton increases and that of the electron decreases — Incorrect. This would need the field along +x. A field along +x would mean that the potential falls along +x. Here the potential rises along +x.
Option (4) The speed of the proton decreases and that of the electron increases — Correct. The force \( e\vec{E} \) on the proton acts along −x, opposite to its velocity, so it slows down. The force \( -e\vec{E} \) on the electron acts along +x, along its velocity, so it speeds up.
NCERT (2026-27):
Relation between Field and Potential – “We thus arrive at two important conclusions concerning the relation between electric field and potential: (i) Electric field is in the direction in which the potential decreases steepest.”