Conductors in electrostatic equilibrium – sharp points, Faraday cage, connected spheres and dielectrics
PhysicsElectric & Magnetic FieldsAges 16–17
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Put a conductor (round, pear-shaped with a sharp tip, a bar or a hollow box) in a uniform electric field and let its free electrons move: they pile up on one side until the field inside is zero, the field lines meet the surface at right angles and the surface charge density σ is greatest at the sharp tip; the hollow box shields its cavity. The Connected spheres screen joins two charged spheres of different radii with a wire, and charge flows until their potentials are equal, q₁/r₁ = q₂/r₂. The Dielectric screen shows a slab polarising, its bound surface charges reducing the field inside by a factor εᵣ.
Lesson: Conductors in electrostatic equilibrium: zero field inside, charge on the outer surface, sharp points and Faraday cages; sharing charge between conductors; dielectrics in an electric field
What it shows
In electrostatic equilibrium the free electrons of a conductor have stopped moving, so the electric field inside the metal is zero. Any excess or induced charge sits on the outer surface, the whole conductor is at one potential, and the field just outside is perpendicular to the surface with E = σ/ε₀. Charge crowds where the surface curves most sharply, which is why lightning rods are pointed. A closed hollow conductor shields its cavity. Two conductors joined by a wire share charge until their potentials are equal. In a dielectric, bound charges on the faces reduce the field to E₀/εᵣ.
How to use
On Conductor in a field, choose the Conductor shape, set External field E₀ and Charge per metre of length λ, then press Let the charges move and watch the field inside fall to zero. Drag the probe and press Record. On Connected spheres, set the radii and starting charges, then press Connect. On Dielectric slab, change Relative permittivity εᵣ or pick Metal and drag the probe across the gap.
Parameters you can change
- Screen Conductor in a field, Connected spheres, Dielectric slab
- Conductor shape Round, Pear (sharp tip), Bar, Hollow box
- External field E₀ 0–5000 V/m
- Charge on the conductor per metre of length λ -30–30 nC/m
- Field lines
- Equipotentials
- Radius of sphere 1 r₁ 1–10 cm
- Radius of sphere 2 r₂ 1–10 cm
- Starting charge q₁ -20–20 nC
- Starting charge q₂ -20–20 nC
- Slab between the plates Dielectric, Metal
- Relative permittivity εᵣ 1–10
Questions to explore
- Why is the electric field inside a metal zero once its charges stop moving?
- Why does a pointed lightning rod collect so much charge at its tip?
- After two spheres are connected, which one has the greater surface charge density, and why?
