What actually is an electric field?

Think of any charged object — a balloon you've rubbed on your jumper, an electron, a proton — as constantly "broadcasting" its presence into the space around it. That broadcast is the electric field. Formally:

Crucially, the charged particle sitting in that field doesn't need to be moving — it feels the force whether it's stationary or in motion. This is a really important distinction from magnetic fields, where a charge only feels a force if it's .

Every charged particle creates its own field, and that field exerts an electrostatic force (F_E) on any other charged particle that happens to be within range. The two golden rules of how charges interact:

• Like charges repel (+ and +, or − and −) — the force pushes them apart.
• Opposite charges attract (+ and −) — the force pulls them together.

And the size of that force isn't fixed — it changes with distance. Charges close together feel a much stronger push or pull than charges far apart. (We'll quantify exactly how much in Coulomb's Law below.)

Measuring "how strong" a field is at a point

Saying "there's an electric field here" is a bit like saying "it's windy outside" — useful, but not precise. To be precise, physicists define electric field strength, E, at a point as:

Why specifically a test charge? Because it fixes the direction convention. If we always imagine dropping a tiny positive charge into the field and asking "which way does it get pushed", then:

• Field lines point away from a positive charge (it repels our positive test charge).
• Field lines point towards a negative charge (it attracts our positive test charge).

E is a vector — it has both a size and a direction, and that direction is exactly the direction of the field lines.

Quantifying attraction and repulsion

We know like charges repel and opposite charges attract — but Coulomb's Law tells us that force is. Think of it like gravity's electric cousin: instead of masses attracting, it's charges pushing or pulling, and the same "inverse square" pattern shows up.

Because of the r² in the denominator, this is called an inverse square law. It means if you double the separation between two charges, the force doesn't halve — it drops to one quarter (½² = ¼) of its original size. Triple the distance and the force falls to just 1/9th. Distance matters a lot.

The sign of F_E tells you the nature of the interaction:

• If Q₁ and Q₂ are opposite signs → F_E comes out negative → attractive force.
• If Q₁ and Q₂ are the same sign → F_E comes out positive → repulsive force.

The radial field

A single point charge (or a charged sphere) produces a radial field — picture field lines spreading out symmetrically in every direction like sun rays, or sucking inward symmetrically for a negative charge.

Notice this is just Coulomb's Law with one of the two charges removed — because here we're not asking "what force acts between two charges", we're asking "how strong is the field itself, independent of what gets placed in it". This equation is only valid for the field around a single point charge (or equivalent sphere) — never use it for parallel plates.

Key features to remember:

• E is not constant in a radial field — it changes with distance.
• It follows an inverse square law (1/r²) — double the distance, and E drops to a quarter.
• If the graph of E against r is plotted, the area under the graph equals the change in electric potential, ΔV.
• For a negative charge, E works out negative — meaning the field vector points the charge.

Linking force-based and energy-based views

So far we've thought about electric fields in terms of . But there's a second, equally powerful way to think about them: in terms of . A positive test charge sitting in a field has electric potential energy due to its position — just like a mass has gravitational PE due to its height.

Moving a positive charge another positive charge takes work (you're fighting the repulsion). Moving it a negative charge also takes work (you're fighting the attraction, effectively "holding it back"). Either way, work done on the charge changes its potential energy.

This links E and V beautifully:

In plain terms:

• If potential changes rapidly with distance → field strength is large.
• If potential changes gradually with distance → field strength is small.

So on a potential-distance (V–r) graph, E is just the gradient at that point. Steep graph = strong field. Flat graph = weak field.

The uniform field

Unlike the radial field around a point charge, the field between two oppositely charged parallel plates is uniform — same strength and same direction at every point between the plates (ignoring the fringing effects right at the edges).

What this tells us:

• Bigger voltage between the plates → stronger field.
• Bigger separation between the plates → weaker field.

The field direction runs from the plate connected to the positive terminal to the plate connected to the negative terminal. If one plate is earthed, treat its voltage as 0 V.

Potential around a point charge

Electric potential (V) is a scalar — no direction — but it does carry a positive or negative sign depending on the charge that's creating it:

• Positive around an isolated positive charge.
• Negative around an isolated negative charge.
• Zero at infinity (this is the reference point).

A handy way to remember the direction of change: potential always decreases in the same direction as the field lines, and increases in the opposite direction.

Field lines and equipotentials

Diagrams are a huge part of this topic, and examiners love testing whether you can draw and interpret them correctly. Two types of lines matter:

• Field lines — show the direction and relative strength of the field. Closer lines = stronger field. Always directed from + to −.
• Equipotential lines/surfaces — join points at the same potential. Always drawn as dotted lines (no arrows — potential is a scalar, it has no direction), and always perpendicular to field lines.

• Field lines: equally spaced, parallel, straight — constant E everywhere between the plates.
• Equipotential lines: horizontal, parallel, equally spaced straight lines.

• Field lines: spread outward (positive) or inward (negative), density decreasing with distance — this decreasing density is what represents E falling off with 1/r².
• Equipotential lines: concentric circles around the charge, spaced progressively further apart as you move outward (because V changes more slowly at greater distances).