Conductors, Symmetry & Shielding
- State the electrostatic properties of a conductor in equilibrium
- Explain why the field inside a conductor and inside a hollow cavity is zero
- Use symmetry to describe the field of a charged sphere, plate and wire
Four properties of a conductor in equilibrium
In electrostatic equilibrium — charges have stopped moving — a conductor satisfies four conditions. The field inside the material is zero, because any field would drive charge until it canceled. All excess charge sits on the outer surface. The field just outside is perpendicular to the surface. And the entire conductor, surface and interior, is a single equipotential. Each of these follows from the same argument: if it were not so, charge would still be moving and the situation would not be static.
Shielding and the Faraday cage
Because the field inside the conducting material is zero, a hollow conductor shields its interior from external fields — charge on the outer surface rearranges to cancel the external field within. This is a Faraday cage, and it is why a car is a reasonably safe place in a lightning strike and why sensitive instruments sit in metal enclosures. Note what it does not do: a charge placed inside the cavity still produces a field there.
Why a uniform sphere acts like a point charge
Outside a spherically symmetric charge distribution, the field is identical to that of a point charge of the same total magnitude at the center. This is why the same kQ/r² serves for a charged ball bearing and a proton. Inside a uniformly charged shell the field is exactly zero — the contributions from all parts of the shell cancel. That result is not obvious and it is worth remembering as a fact, because it underlies both shielding and the shell theorem in gravitation.
Charge concentrates where curvature is high
On an irregular conductor, surface charge density is greatest where the surface is most sharply curved — at points and corners. Since the external field just outside is proportional to that density, the field is strongest at sharp points too. This is why lightning rods are pointed, and why high-voltage equipment uses rounded surfaces to avoid the corona discharge that intense local fields produce.
A hollow conducting sphere of radius 0.10 m carries a net charge of +6.0 nC. Find the field at r = 0.05 m, at r = 0.20 m, and describe the potential inside.
- 1.At r = 0.05 m — inside the conducting shell: E = 0, since the field inside a conductor in equilibrium is zero.
- 2.At r = 0.20 m — outside: the sphere acts as a point charge at the center.
- 3.E = kQ/r² = (8.99 × 10⁹)(6.0 × 10⁻⁹)/(0.20)² = 1350 N/C, directed radially outward.
- 4.Potential inside: constant, and equal to the surface value kQ/R = (8.99 × 10⁹)(6.0 × 10⁻⁹)/0.10 = 539 V.
Zero field does not mean zero potential. Inside a charged conductor the field is zero but the potential is a constant nonzero value, because potential is set by the work needed to bring a charge in from infinity, not by the local field.
The electric field inside the material of a conductor in electrostatic equilibrium is zero because:
A point charge is placed at the center of a hollow, uncharged conducting shell. Outside the shell, the field is:
On an irregularly shaped charged conductor, the surface charge density is greatest:
For a symmetric charged object, state which region you are in before writing any formula — inside a conductor, inside a cavity, or outside. Each region has a different answer, and using the outside formula inside is the standard error.
Answer the 3 checkpoints as you read.
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