Two point charges exert a force on each other along the line joining them: like charges repel and unlike charges attract. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
k = 8.99 × 10⁹ N m² C⁻² (ε₀ = 8.85 × 10⁻¹² F/m). Charges in coulombs, r in metres.
Try itThe force between two charges
Choose two charges and their separation. Find the force between them.
Electric field and potential
The electric field strength E at a point is the force per unit positive charge placed there (N/C or V/m). Field lines show the direction of the force on a positive charge: they leave positive charges and end on negative charges. The closer the lines, the stronger the field. The electric potential V at a point is the work done per unit positive charge in bringing it from infinity to the point (volts).
The field is the negative gradient of the potential. Between parallel plates the field is uniform.
Worked exampleField between plates
Two parallel plates 2.0 cm apart have a voltage of 400 V between them. Find the electric field strength, and the force on an electron between them. (e = 1.6 × 10⁻¹⁹ C)
Electric field.
Force on the electron.
Answer: The field is 2.0 × 10⁴ V/m and the force on the electron is 3.2 × 10⁻¹⁵ N.
Capacitors and energy
A capacitor’s capacitance depends on plate area A, plate separation d and the dielectric (relative permittivity εᵣ). Energy stored is the area under a V–Q graph.
Combination
Total capacitance
In parallel
C = C₁ + C₂ + …
In series
1/C = 1/C₁ + 1/C₂ + …
The voltage follows V = V₀(1 − e^(−t/RC)) when charging and V = V₀e^(−t/RC) when discharging.
Application
Idea
Photocopier and laser printer
Charged drum attracts toner powder
Lightning conductors
Points discharge the charge in the air gently
Electrostatic precipitator
Charged plates remove smoke particles from factory chimneys
Paint spraying
Charged droplets are attracted to the object and coat it evenly
Van de Graaff generator
Builds up a large charge on a dome
Key terms
Electric field strength
The force per unit charge at a point.
Electric potential
The work done per unit charge in bringing a positive charge from infinity.
Capacitance
The charge stored per unit voltage.
Dielectric
An insulator between the plates of a capacitor.
Summary
Coulomb's law F = kQ₁Q₂ ÷ r².
E = F/q = kQ/r²; V = kQ/r; E = V/d between parallel plates.
C = Q/V; energy ½CV²; series and parallel combinations.
Charging and discharging are exponential with time constant RC.
