Describe electric fields and potential and apply them to point charges and uniform fields between parallel plates

What this dot point is asking

WACE treats electric fields as a direct parallel to gravitational fields, with the key differences that charge comes in two signs and the force can attract or repel. You need to handle both the point-charge case and the uniform-field-between-plates case, and connect field, force, work and potential difference.

Coulomb's law and the field of a point charge

The force between two point charges is

Like charges repel; opposite charges attract. The electric field strength is the force per unit positive charge,

Field is a vector, pointing away from positive source charges and toward negative ones. Field lines never cross, and their density represents field strength.

The uniform field between parallel plates

Two oppositely charged parallel plates produce a uniform field (except near the edges). Its magnitude is

where $V$ is the potential difference across the plates and $d$ their separation. Here the units $\text{V m}^{-1}$ and $\text{N C}^{-1}$ are equivalent. The field points from the positive plate to the negative plate, and the force $F=qE$ on a charge is constant throughout the gap.

Work and potential difference

Potential difference is the work done per unit charge moved between two points,

When a charge is accelerated from rest through a potential difference, that work becomes kinetic energy,

so $v=\sqrt{\dfrac{2qV}{m}}$. This is the standard electron-gun calculation.

Motion of a charge in a uniform field

A charged particle entering a uniform field experiences a constant force, so its path is a parabola in exactly the same way a projectile is. The component along the field accelerates uniformly while the perpendicular component stays constant. This deflection of charges is the basis of cathode-ray tubes and is a favourite exam scenario.

Field as a parallel to gravity

WACE deliberately mirrors electric fields with gravitational fields so you can transfer reasoning. Gravitational field strength $g=GM/r^2$ is force per unit mass; electric field strength $E=kQ/r^2$ is force per unit charge. Both are inverse-square radial fields, both are vectors, and both give a constant uniform field in special geometries (near a planet's surface for gravity, between parallel plates for electricity). The decisive difference is that mass is single-signed so gravity only attracts, whereas charge has two signs so the electric field can point toward or away from a source and forces can repel. Carrying this analogy explicitly into an answer earns marks and helps you remember which formula has which constant.

Field lines and equipotentials

Field lines start on positive charges and end on negative charges, and they are always perpendicular to surfaces of equal potential (equipotentials). Between parallel plates the field lines are parallel and evenly spaced, so the equipotentials are flat planes parallel to the plates. Around a point charge the lines are radial and the equipotentials are concentric spheres. Because no work is done moving a charge along an equipotential (there is no potential difference between its points), the force has no component along it, which is exactly why field lines and equipotentials meet at right angles.

Linking the field and potential pictures

A graph of $E$ against $r$ for a point charge falls as $1/r^2$, while a graph for parallel plates is flat. The work done moving a charge equals $q$ times the change in potential, which is the area interpretation you may be asked to use. Keep clear which scenario you are in before choosing a formula.