Electrostatics with Conductors
Introduced| English |
|---|
| electrostatic equilibrium/ɪˌlektrəʊˈstætɪk ˌiːkwɪˈlɪbrɪəm/ |
| Faraday cage/ˈfærədeɪ keɪdʒ/ |
Why is a metal car one of the safest places in a lightning storm?
- Lightning hits the car, yet the people inside are unharmed.
- A conductor wraps its passengers in a charge-free, field-free space.
- The metal's free electrons rearrange in an instant to cancel the field inside.
- This lesson is about how conductors behave once the charges stop moving.
No field inside, in equilibrium
- Once charges settle (electrostatic equilibrium 静电平衡), the field inside a conductor is zero.
- If it weren't, the free charges would feel a force and keep moving — not settled.
- So $E = 0$ everywhere inside the metal.
- Any cavity inside is shielded too — that is a Faraday cage 法拉第笼.
Inside a conductor in electrostatic equilibrium, the electric field is:
If it were not zero, free charges would move — so at equilibrium $E = 0$ inside.
A hollow conductor shields its inside from external fields (a Faraday cage).
The conductor cancels the field inside the cavity — a Faraday cage.
All charge lives on the surface
- Because the inside field is zero, no net charge can sit inside.
- Every bit of excess charge is pushed to the surface.
- Gauss's law confirms it: any interior Gaussian surface encloses zero charge.
- The charge spreads to make the whole conductor one potential.
Excess charge on a solid conductor sits:
With zero interior field, all excess charge must lie on the surface.
The field just outside
- Just outside the surface, the field is perpendicular to it.
- A parallel field would push surface charges sideways — but they've stopped.
- Its size is $E = \dfrac{\sigma}{\varepsilon_0}$, set by the local surface charge density $\sigma$.
- Flat inside, purely perpendicular outside.
A charged conductor at equilibrium
Sort each statement about a conductor in electrostatic equilibrium.
Just outside a conductor's surface, the field is ____ to the surface.
A parallel component would move surface charges, so $E$ is perpendicular.
Select all true statements about a conductor in equilibrium.
Zero interior field, surface charge, single potential. Charge never fills the volume.
Charge crowds at sharp points
- On a lumpy conductor, charge piles up where the surface curves sharply.
- Sharp points have the highest $\sigma$ and the strongest field.
- That is why lightning rods are pointed — the field there ionises the air first.
- Smooth, round shapes spread charge more evenly.
On a conductor, charge and field are strongest at:
Charge crowds at sharp points, giving the highest $\sigma$ and field.
You sit inside a metal cage as a charged rod touches the outside.
- The charge spreads over the cage's outer surface.
- Inside, $E = 0$, so you feel nothing — the cage shields you.
"$E = 0$ inside" holds only in electrostatic equilibrium — after the charges have settled. During the split-second of rearranging, fields inside are not zero. And it applies to the conductor's material, not to a charge you place in a hollow cavity.
In electrostatic equilibrium a conductor has $E = 0$ inside, so all excess charge sits on the surface and the whole conductor is one potential. Just outside, $E = \sigma/\varepsilon_0$ and is perpendicular to the surface; charge crowds at sharp points.