Two conducting spheres joined by a wire.

Two conducting spheres joined by a thin wire: charge shares until the potentials match, leaving the smaller sphere with the larger σ and surface field.

Choose radii so the small sphere's surface field is three times the large sphere's (radius ratio 1 : 3)

Thinking charge shares to equal charge or equal density rather than equal potential.

• Metals have free electrons that can move inside the metal but cannot leave it. In a field they drift opposite to the field until the field inside falls to zero.
• In the static state the electric field inside a conductor is zero everywhere, whether it is neutral or charged and whatever the outside field.
• Just outside a charged conductor the field is normal to the surface at each point; a component along the surface would push the surface charges.
• A conductor can hold no excess charge in its interior; Gauss's law on any small closed surface inside gives zero enclosed charge, so all excess charge sits on the surface.
• The whole conductor, inside and on its surface, is at one potential. Different conductors in a system can be at different potentials.
• Field just outside a charged conductor: E = (σ/ε₀) n̂, where σ is the local surface charge density and n̂ the outward normal (inward for σ < 0).
• Electrostatic shielding: a cavity inside a conductor, with no charge in it, has zero field whatever the charges and fields outside. This protects sensitive instruments.
• Shielding works only one way: a charge placed inside a cavity still produces a field outside the conductor.
• Everyday cases: aircraft tyres made slightly conducting and fuel tankers trailing metal chains let friction charge drain to earth before it can spark.

Teaching this idea? Put the simulation on your own page or LMS with this code.