Quick questions on Charged particles in electric fields explained: HSC Physics Module 6

Two parallel conducting plates held at a potential difference $V$ and separated by a distance $d$ produce a nearly uniform electric field in the region between them:

A particle of charge $q$ in the field experiences a force:

If the charge moves a distance $d$ in the direction of the field (or, equivalently, through a potential difference $V$ between its start and end positions):

By the work-energy theorem, the work done by the net force equals the change in kinetic energy:

Parallel acceleration. The particle enters along the field direction (or starts at rest). Motion is one-dimensional, constant acceleration. Use $v^2 = u^2 + 2as$ with $s = d$, or use energy: $qV = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2$.

The particle enters along the field direction (or starts at rest). Motion is one-dimensional, constant acceleration. Use $v^2 = u^2 + 2as$ with $s = d$, or use energy: $qV = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2$.

The particle enters horizontally between the plates with speed $v_x$, and the field is vertical. The horizontal speed is constant, the vertical motion has constant acceleration $a = qE/m$. After time $t = L / v_x$ in plates of length $L$, the vertical deflection is $y = \frac{1}{2} a t^2$.

The force on a negative charge is $-|q|E$, so an electron near a negative plate is pushed toward the positive plate.

$E = V/d$ requires $d$ in metres. A 5 cm gap is 0.05 m, not 5.

The $d$ in $W = qEd$ is the distance moved along the field. Transverse motion does no work; only the component of displacement along $E$ counts.

For electrons and protons in the electric fields of standard HSC problems, the gravitational force is many orders of magnitude smaller than the electric force and is usually neglected. State this assumption explicitly if asked.

$V$ is the potential difference through which the charge moves; a positive charge gains kinetic energy when moving from high to low potential, a negative charge gains kinetic energy when moving from low to high potential.