Revise Electric potential for Cambridge 9702 (18.5)

Electric potential ($V$) at any point in an electric field is fundamentally defined as the amount of work done per unit positive test charge. This work is performed by an external force to slowly move a tiny positive test charge from an infinitely distant point (where potential is considered zero) to the specific point you're interested in, without causing any acceleration. Think of it as the electric potential energy that each coulomb of charge would possess at that location.

$V = \frac{W}{Q}$

For an isolated point charge, the electric field it creates is radial. The electric potential at a distance $r$ from this charge depends directly on the charge's magnitude and inversely on the distance. This formula describes the absolute potential created by a single point charge in a vacuum or air.

$V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$

While electric potential is energy per unit charge, electric potential energy ($U$) is the total work done to bring a specific charge from infinity to a point in an electric field. If you have two point charges, $Q_1$ and $Q_2$, separated by a distance $r$, this formula gives the potential energy stored in their configuration. It's the work required to assemble them from infinite separation.

$U = \frac{Q_1Q_2}{4\pi\epsilon_0 r}$

When a charge moves from one point to another within an electric field, if there's a difference in electric potential between these points, work will be done either by the field or on the charge. The amount of work done depends on the charge's magnitude and the potential difference it traverses.

$W = Q\Delta V$

Equipotential lines (or surfaces in 3D) are incredibly useful visual tools. They represent all the points in an electric field that share the exact same electric potential. Imagine contour lines on a map, but for electrical 'height'. A crucial property is that if a charge moves along an equipotential line, no work is done by the electric field, because there's no change in potential energy ($\\Delta V = 0$).

A special case is a uniform electric field, typically found between two large, parallel conducting plates with opposite charges. In such a field, the electric field strength is constant in magnitude and direction. This simplifies the relationship between electric field strength and potential difference significantly.

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