What is an electric field?

A charge creates a field around itself

Any electric charge Q alters the space around it: at every point, it creates an electric field, denoted by E, which represents the effect it would have on another charge placed at that point. The field exists even if no charge is present to ‘feel’ it: it is a property of space due to Q.

Definition based on force

If a charge q is placed at a point M where a field E is present, it experiences an electric force F = q * E. The field at this point is therefore defined as:

E = F / q (in volts per metre, V/m)

The field created by a point charge

A point charge Q, isolated in a vacuum, creates a field at a point M situated at a distance r, the magnitude of which is:

E = k * |Q| / r^2

where k = 9 × 10^9 N·m^2/C^2 (Coulomb’s constant).

The field is directed:

• away from Q if Q > 0 (‘outgoing’ field)
• towards Q if Q < 0 (‘incoming’ field)

Example

For a charge Q = 2 × 10⁻⁶ C, at a distance r = 0.1 m:

E = 9 × 10⁹ × 2 × 10⁻⁶ / (0.1)² = 1.8 × 10⁶ V/m

Common pitfall

Do not confuse the charge that CREATES the field (Q) with the charge that EXPERIENCES IT (q, known as the ‘test charge’). The field E does not depend on q: it is a property of point M, determined by Q.