How charges at rest create fields, potential and stored energy
Electric charge is quantised, coming in whole multiples of e = 1.6 × 10⁻¹⁹ C, and it is conserved. Coulomb’s law gives the force between two point charges: F = kq₁q₂/r², where k = 1/(4πε₀) ≈ 9 × 10⁹ N m² C⁻². The electric field E at a point is the force per unit positive charge, and field lines show its direction. Gauss’s law states that the total electric flux through any closed surface equals the enclosed charge divided by ε₀, which makes fields of spheres, wires and sheets easy to find.
Electric potential is the work done per unit charge in bringing a test charge from infinity, V = kq/r for a point charge. A capacitor stores charge and energy; for a parallel-plate capacitor, C = ε₀A/d, and inserting a dielectric of constant K multiplies C by K. Capacitors in parallel add directly, while in series their reciprocals add. The energy stored is U = ½CV².
Why it matters
Capacitors smooth power supplies, store energy for camera flashes and form the touch sensors in phone screens. Lightning conductors, photocopiers and electrostatic paint sprayers use the behaviour of static charge. The ideas of field and potential introduced here are used throughout current electricity, magnetism and electromagnetic waves.
Key terms
- Coulomb’s law
- The force between two point charges is proportional to the product of the charges and inversely proportional to the square of their distance.
- Electric field
- The force experienced per unit positive test charge at a point in space.
- Equipotential surface
- A surface on which every point has the same electric potential, so no work is done moving a charge along it.
- Dielectric
- An insulating material that, placed between capacitor plates, increases the capacitance.