AP® Physics 2: Algebra-Based · Unit 10 · Topic 10.3
Fields Inside and Around Conductors
Inside a conductor in equilibrium, the electric field is always exactly zero because free electrons rearrange themselves until they cancel it out, and any excess charge ends up on the outer surface.
A conductor is full of free electrons that can slide around inside the material. If any electric field existed inside the conductor, it would push on those electrons, and they would move. They keep moving and rearranging themselves until their own field exactly cancels whatever external or internal field was pushing them. The instant the net field inside hits zero, there's no more force to move them, so they stop. That's not a special property of metal, it's just what "equilibrium" means for charges free to move: zero field inside is the only stable arrangement.
This same shuffling explains where excess charge goes on a solid charged conductor, like a metal ball. If any extra charge sat inside the body of the conductor, it would create a field there, which would push nearby free electrons until that field vanished, shoving the charge outward. This keeps happening until every bit of excess charge has migrated to the outer surface, the only place it can sit without creating a field inside the metal. Inside, you're left with zero field and zero net charge; all the charge and all the field action happen at the boundary.
An insulator can't do any of this. Its charges are bound to atoms and can't roam to cancel a field, so a charged insulator generally keeps a nonzero field threaded through its interior. This contrast connects directly to the next idea in the unit: field lines meeting a conductor's surface always hit it perpendicular, and the field just outside is strongest where surface charge is most crowded together, which sets up the next topic on sharp points and charge density.
Key terms
- Conductor
- A material with free electrons that can move through it in response to an electric field.
- Electrostatic equilibrium
- The state a conductor reaches when its free charges have stopped moving and the internal field is zero.
- Surface charge density
- The amount of excess charge per unit area on a conductor's surface, often written as sigma.
- Insulator
- A material whose charges are bound to atoms and cannot move freely to cancel an internal field.
Watch it explained
- How it worksHow do free electrons rearrange themselves until the field inside a conductor is exactly zero?
- How it worksWalk me through why excess charge on a solid metal ball ends up entirely on its outer surface.
- Common mistakeWhy isn't the field inside a charged insulator zero the way it is inside a conductor?
- Going furtherWhat happens to the surface charge density at a sharp point on a charged conductor?
Check yourself
End of topic.