Electric field between two plates

Problem statement

Two parallel plates have been placed perpendicular to the $x$ direction. One of them has been given a positive charge and the other an equal charge of negative sign. Using a probe, the electrostatic potential has been measured in the region between the plates, $0\le x\le 10$ m. From the measurements it has been determined that the potential in that interval is given by $V(x)=-3x$, with $x$ in metres and $V$ in volts. The electric field strength is related to the potential, in the one-dimensional case, by $E(x)=-\dfrac{dV}{dx}$.

a) (1 mark) Calculate the electric field in the interval $0\le x\le 10$ m.

b) (0.5 marks) Determine the acceleration of a charge of 10 nC and mass $6\cdot10^{-10}$ kg placed at the point $x=5$ m.

c) (1 mark) If the charge of 10 nC and mass $6\cdot10^{-10}$ kg is released from rest at the origin, determine its speed at the point $x=5$ m.

Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Physics · Question 1. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.