Instead of describing a separate force law for every test charge, we can describe the influence produced by source charges throughout space. The electric field is force per unit positive test charge:

$$\mathbf E=\frac{\mathbf F}{q}.$$

A charge $q$ placed in an existing field experiences

$$\mathbf F=q\mathbf E.$$

For a negative charge, the force points opposite to the field.

Field of a point charge

A point charge $Q$ produces

$$\mathbf E=\frac1{4\pi\varepsilon_0}\frac{Q}{r^2},\hat{\mathbf r},$$

where $\hat{\mathbf r}$ points away from the source. Positive charges produce outward fields and negative charges inward fields.

Superposition

Electric fields add as vectors:

$$\mathbf E_{\mathrm{total}}=\sum_i\mathbf E_i.$$

The field therefore depends only on the source configuration, while the force additionally depends on the charge placed in that field.

Field lines

Electric-field lines are a visualization: their tangent direction gives the field direction and denser lines conventionally represent stronger fields. They are not physical threads in space.