Electric fields

What it is

An electric field describes what force a charge would feel if it were placed at a given point. The field is there wherever there are charges around, even with no test charge in place. Field strength is force per charge, E = F/q, measured in N/C (or V/m). Because force has direction, the field is a vector at each point; see electric field strength. The direction is that of the force on a positive test charge: away from positive charges and toward negative ones.

Examples:

• A test charge. If a charge q = 4.0 · 10⁻⁶ C feels a force F = 2.0 · 10⁻³ N, the field strength there is E = 2.0 · 10⁻³/4.0 · 10⁻⁶ = 500 N/C.
• Around a point charge. The field points straight out from a positive charge and is a quarter as strong at twice the distance; see electric field from a point charge.
• Between two plates. The field is nearly the same everywhere: 100 V across 0.020 m gives E = U/d = 5 000 V/m = 5 000 N/C; see uniform electric field. An electron there feels a force eE = 1.602176634 · 10⁻¹⁹ · 5 000 ≈ 8.0 · 10⁻¹⁶ N; see charge in an electric field.
• Several charges. Fields add as vectors. Two perpendicular fields of 3 N/C and 4 N/C give 5 N/C.

Field lines are drawn from positive toward negative charges. Close lines mean a strong field; a line shows the direction of the force on a positive test charge.

What is not an electric field:

• The force on the charge. The field is force per charge, so it is still there if you remove the charge; the force is not.
• Voltage. A volt is energy per charge, while V/m is field strength. See electric potential.
• The gravitational field. That is a different field with the same idea: g = F/m in N/kg; see gravitational field strength.

Why it matters

The field idea lets us work with a charge’s surroundings instead of with every charge separately. Knowing the field at a point gives the force on any charge there by F = qE. That is how Coulomb’s law is used in practice, and it is the starting point for capacitors, electron beams and the motion of charged particles. The same idea returns for magnetic fields and, with the field in motion, for electromagnetic waves.

Common misconceptions

• “Field lines are paths that charges follow.” A line gives the direction of the force at each point. A charge that is already moving does not necessarily follow the line.
• “The field inside a conductor is strong.” In equilibrium the field inside a conductor is zero.
• “The field becomes zero at a large distance.” It weakens but is never exactly zero outside the charge; around a point charge it falls as 1/r².

Common questions