Revise Uniform electric fields for Cambridge 9702 (18.2)

A uniform electric field is a special region where the electric force on a charged particle is the same in both strength and direction, no matter where the particle is located within that region. This consistency is represented visually by straight, parallel, and equally spaced electric field lines.

At its core, electric field strength (E) quantifies the force exerted per unit of positive charge. This fundamental definition applies to all electric fields, uniform or not. When a charge 'q' is placed in a field 'E', it experiences a force 'F'.

$E = F/Q$ or $F = Eq$

The most common way to create a uniform electric field is by applying a potential difference ($\Delta V$) across two large, parallel metal plates separated by a distance ($d$). The field lines emerge perpendicularly from the positive plate and terminate perpendicularly on the negative plate.

$E = \frac{\Delta V}{d}$

This formula highlights that the electric field strength is also the magnitude of the potential gradient. It means for every metre you move across the field, the electric potential changes by 'E' Volts. The units for electric field strength can therefore be N C⁻¹ or V m⁻¹.

Imagine contour lines on a map showing points of equal height. Equipotential surfaces (or lines in 2D) are similar, connecting all points within the field that have the same electric potential. In a uniform field, these are simple.

When a charged particle enters a uniform electric field, it experiences a constant force ($F=Eq$), much like the constant gravitational force on a mass near the Earth's surface. According to Newton's second law, this constant force produces a constant acceleration ($a=F/m = Eq/m$). This allows us to use the standard kinematic equations (suvat) to predict the particle's motion. The trajectory depends on the initial velocity relative to the field.