Electric fields

Electric fields are vector quantities that describe the force per unit charge at each point in space around a source charge. The field points away from positive sources and toward negative sources, and the force on a positive test charge is in the same direction as the field. When multiple charges are present, the net electric field at any point equals the vector sum of the individual contributions from each charge — this is superposition. Electric field maps and field line diagrams provide visual representations: vector arrows show magnitude by their length, while field lines show magnitude by their spacing and direction by their tangent.

Conductors

• Has zero electric field throughout its interior when in electrostatic equilibrium
• Carries all of its excess charge on its surface
• Has a surface field that is perpendicular to the surface at every point

Outside an isolated charged sphere with spherical symmetry, the field is identical to that of a point charge located at the center, decreasing as 1/r²:

E = 1/4πε₀Q/r² = kQ/r² ∝ 1/r²

Insulators

• Can hold charge throughout its volume because its charge carriers are not free to move
• May have a nonzero internal field, determined by the specific distribution of charge within the material