Key ideas
Electrostatics deals with the forces and energy of charges at rest. Like charges repel and unlike charges attract, and the force falls off with the square of the distance.
- Coulomb’s law is F = kq₁q₂ ÷ r², with k = 8.99 × 10⁹ N·m²/C². The force is along the line joining the charges.
- The electric field E is the force per unit charge. It is a vector, and fields from several charges add as vectors.
- Electric potential V is energy per unit charge. It is a scalar, so potentials from several charges add as plain numbers.
- A capacitor of capacitance C at voltage V stores charge Q = CV and energy ½CV²; for parallel plates C = ε₀A ÷ d.
Key equations
F = kq₁q₂ ÷ r²E = F ÷ q = kQ ÷ r²V = kQ ÷ rU = qVC = ε₀A ÷ dU_C = ½CV²
Worked example
Two charges, 2.0 μC and 3.0 μC, are 0.30 m apart. F = (8.99 × 10⁹) × (2.0 × 10⁻⁶)(3.0 × 10⁻⁶) ÷ 0.30² = 0.054 ÷ 0.090 = 0.60 N, and it is repulsive because the charges have the same sign. If the distance is doubled, the force drops to 0.15 N.
Common mistakes
- Forgetting to square the distance, or using the distance in centimeters without converting.
- Leaving charges in μC or nC without converting to coulombs.
- Adding potentials as vectors or fields as plain numbers. Fields are vectors, potentials are scalars.
Practice
Test yourself with practice questions on this topic: Electrostatics