Electric field vector: direction, sense and superposition

A field is a vector

At every point in space, the electric field E is characterised by:

• a direction (the line along which the vector lies)
• a sense (towards or away from the source charge)
• a magnitude (intensity, in V/m)
• a point of application (the point M under consideration)

E is represented by an arrow originating from M.

Field lines

A field line is a curve that is tangent to the vector E at every point. For a point charge, the field lines are radial half-lines: they diverge from a positive charge and converge towards a negative charge.

Type of charge	Direction of the field	Field lines
Q > 0	moves away from Q	divergent
Q < 0	moves towards Q	convergent

Principle of superposition

When several charges are present, the total field at a point is the vector sum of the fields created by each charge:

E_total = E1 + E2 + ... + En (vector addition, not just magnitudes!)

Example

Two identical charges Q, placed symmetrically about a point M lying on the perpendicular bisector of the line segment connecting them: the components perpendicular to the s-axis cancel each other out; only the components along the s-axis add together.

Common pitfall

Directly adding the magnitudes (E1 + E2) without taking the directions into account is a common mistake. Each vector must be decomposed into components along the common axes (x, y) before summing, unless the fields are collinear and in the same direction.