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An electric field is a region of space in which a charged particle experiences a force. This concept is central to understanding how charges interact at a distance, and it underpins everything from simple circuits to particle accelerators.
Electric field strength (E) is defined as the force per unit positive charge placed at that point:
E = F / Q
where F is the force in newtons (N) and Q is the charge in coulombs (C). The unit of electric field strength is N C⁻¹ (newtons per coulomb), which is equivalent to V m⁻¹ (volts per metre).
Electric field strength is a vector quantity — it has both magnitude and direction. By convention, the direction of the electric field is the direction in which a positive test charge would move if placed in the field. This means field lines point away from positive charges and towards negative charges.
Electric field lines are a visual tool for representing the direction and relative strength of an electric field.
Rules for field lines:
A point charge (or a charged sphere, when viewed from outside) produces a radial field. The field lines spread outward in all directions from a positive charge (or converge inward towards a negative charge). The field strength decreases with distance from the charge — the lines spread further apart.
Between two parallel plates connected to a potential difference, the electric field is uniform. The field lines are parallel, equally spaced, and perpendicular to the plates. This means the field strength is the same at every point between the plates (ignoring edge effects).
For a uniform field between parallel plates separated by a distance d with a potential difference V across them:
E = V / d
This is an extremely useful relationship. It tells you that doubling the voltage doubles the field strength, and doubling the plate separation halves it.
Two parallel plates are separated by 5.0 cm and have a potential difference of 2000 V across them. Calculate the electric field strength between the plates.
E = V / d = 2000 / 0.050 = 40 000 V m⁻¹ = 4.0 × 10⁴ V m⁻¹
Note the conversion of 5.0 cm to 0.050 m — always work in SI units.
The direction of the electric field is defined as the direction a positive charge would accelerate. This means:
When solving problems involving negative charges (such as electrons), remember that the force on the charge is in the opposite direction to the field. An electron placed in a uniform field between parallel plates accelerates towards the positive plate — against the field direction.
Rearranging E = F / Q gives:
F = EQ
For a uniform field (E = V / d), this becomes:
F = VQ / d
This force is constant throughout the uniform field, meaning a charged particle between parallel plates experiences a constant acceleration — exactly like a mass in a uniform gravitational field near the Earth's surface.
An electron (charge = 1.6 × 10⁻¹⁹ C, mass = 9.11 × 10⁻³¹ kg) enters a uniform electric field of strength 5.0 × 10³ V m⁻¹. Calculate the force on the electron and its acceleration.
Force: F = EQ = 5.0 × 10³ × 1.6 × 10⁻¹⁹ = 8.0 × 10⁻¹⁶ N
Acceleration: a = F / m = 8.0 × 10⁻¹⁶ / 9.11 × 10⁻³¹ = 8.8 × 10¹⁴ m s⁻²
This is an enormous acceleration — roughly 10¹⁴ times greater than g. This illustrates why electric forces dominate over gravitational forces at the atomic and subatomic scale.
There is a close analogy between electric and gravitational fields:
| Property | Electric Field | Gravitational Field |
|---|---|---|
| Field strength definition | Force per unit charge (E = F/Q) | Force per unit mass (g = F/m) |
| Uniform field | Between parallel plates | Near Earth's surface |
| Radial field | Around a point charge | Around a point mass |
| Field lines | Start on +, end on − | Always point towards mass |
| Force can be | Attractive or repulsive | Attractive only |
This analogy is helpful throughout this topic. Many of the mathematical relationships have the same structure, differing only in whether they involve charge or mass.