What a conductor does in a field
Conductors contain mobile charge carriers. In a metal the outer valence electrons part away from their atoms and are free to move within the metal, though not free to leave it. These free electrons form a kind of gas; they collide with each other and with the fixed positive ions and move randomly in different directions. The positive ions, made of the nuclei and the bound electrons, stay held in their fixed positions.
Place such a conductor in an external electric field $\vec{E}$ and the free electrons immediately drift against the direction of the field. Negative charge piles up on one face and the opposite face is left positive. These induced charges set up their own field inside the conductor, opposing the external one. The drift continues until the internal field they create exactly cancels the applied field. This balanced state — no net transfer of charge from one part to another — is called electrostatic equilibrium, and for a metal it is reached almost instantaneously, in the order of $10^{-16}\ \text{s}$.
Everything that follows assumes the conductor has settled into this static state. We restrict the discussion to metallic solid conductors, exactly as NCERT does.
Field is zero inside
The first and most important result: in the static situation the electric field is zero everywhere inside the conductor, whether the conductor is neutral or charged, and whether or not an external field is present. NCERT treats this as the defining property of a conductor in the static state.
The argument is short. A conductor has free electrons. As long as the field inside is not zero, those free charges feel a force and drift. Drift means the charges are not yet in equilibrium. So equilibrium — by definition the static situation — can only be the configuration in which the free charges have arranged themselves to make the field zero everywhere inside. The redistribution stops precisely when $\vec{E}_{\text{inside}} = 0$.
A charged conductor in equilibrium: field cancels inside, charge sits on the surface.
Field at the surface: normal and sigma/epsilon-zero
Just outside the surface of a charged conductor the field cannot be zero, but it is tightly constrained. The electrostatic field at the surface must be normal to the surface at every point. If $\vec{E}$ had any component along the surface, the surface charges would feel a tangential force and move — which contradicts the static situation. So in equilibrium the tangential component is zero and the field stands perpendicular to the surface everywhere.
Its magnitude follows from Gauss's law. Choose a tiny pill box — a short cylinder of cross-section $\delta S$ and negligible height — straddling the surface, half inside and half outside. Inside, the field is zero, so no flux passes through the inner face. The field is normal to the surface, so the curved side contributes nothing. Only the outer face contributes flux $E\,\delta S$, and the charge it encloses is $\sigma\,\delta S$. Gauss's law gives
$$ E\,\delta S = \frac{\sigma\,\delta S}{\varepsilon_0} \quad\Rightarrow\quad \vec{E} = \frac{\sigma}{\varepsilon_0}\,\hat{n} $$where $\sigma$ is the local surface charge density and $\hat{n}$ is the outward normal. For $\sigma > 0$ the field points outward; for $\sigma < 0$ it points inward. Where there is no surface charge the field is zero even at the surface.
Gaussian pill box at the surface: only the outer face has flux, giving E = sigma/epsilon-zero, normal to the surface.
Charge resides on the surface
A neutral conductor carries equal positive and negative charge in every small element. When you give it an excess charge, that excess can only reside on the surface in the static situation. This too follows from Gauss's law. Take any arbitrary volume element inside the conductor, bounded by a closed surface $S$. Because the field is zero everywhere inside, the total flux through $S$ is zero, so the net charge enclosed is zero. The volume can be shrunk to be vanishingly small around any interior point, so there is no net charge anywhere inside — every bit of excess charge sits on the surface.
Each result here rests on the idea that a constant potential means a vanishing field. Revisit Equipotential Surfaces to see why field lines must cross them at right angles.
The conductor is an equipotential volume
Combine the first two results. Inside, $\vec{E} = 0$; on the surface, the field has no tangential component. So no work is done in moving a small test charge anywhere within the conductor or along its surface, which means there is no potential difference between any two such points. Therefore the electrostatic potential is constant throughout the volume of the conductor and equals the value on its surface. The whole body — interior and surface together — is one equipotential.
If the conductor is charged, a normal field $\sigma/\varepsilon_0$ exists just outside, so the potential of a point just outside the surface differs from the constant value on the conductor. In a system of several conductors of arbitrary size, shape and charge, each conductor is characterised by its own constant potential, but that constant may differ from one conductor to another.
"Field zero inside" does not mean "field zero just outside"
The interior field is exactly zero, but the field just outside a charged surface is $\sigma/\varepsilon_0$ along the normal. The field jumps discontinuously across the surface, from $0$ to $\sigma/\varepsilon_0$. Examiners pair these two facts in the same option to catch a hurried read.
Inside: $\vec E = 0$. Just outside: $\vec E = \dfrac{\sigma}{\varepsilon_0}\hat n$, normal to the surface.
Equipotential volume, not just an equipotential surface
A charged conductor's surface being an equipotential is the easy half. The stronger statement is that the entire interior sits at the same potential as the surface. Because $V$ is constant through the volume, $\vec E = -\nabla V = 0$ inside — which is exactly why "V constant in a region" forces "E = 0 there".
If $V$ is the same at every point of a region, the field is zero throughout that region.
Electrostatic shielding and the Faraday cage
Now consider a conductor with a cavity that contains no charge. A remarkable and very general result holds: the electric field inside the cavity is zero, whatever the size and shape of the cavity, whatever the charge on the conductor, and whatever external field the conductor is placed in. A special case — the field inside a charged spherical shell being zero — was proved earlier using spherical symmetry, but the cavity result needs no symmetry at all.
A related fact: even if the conductor is charged, or charge is induced on a neutral conductor by an external field, all the charge resides only on the outer surface of a conductor with a cavity; the cavity wall stays bare. The cavity therefore remains shielded from any outside electric influence — this is electrostatic shielding. It is exploited to protect sensitive instruments from external fields, and it is why a metallic car or bus body keeps its occupants safe during a lightning storm, far safer than standing in the open. The hollow conductor enclosing a protected region is the Faraday cage.
Electrostatic shielding: an external field induces surface charge, but the cavity field stays zero.
Shielding works one way for an empty cavity
The zero-field cavity result holds when there is no charge inside the cavity. The cavity is shielded from whatever happens outside. Do not extend it to claim a charge placed inside the cavity has no effect outside — that is a different situation. For the standard NEET statement, keep to NCERT's wording: an empty cavity in a conductor has zero field, irrespective of the conductor's charge or any external field.
Empty cavity ⇒ field inside it is zero; charge resides only on the outer surface.
Surface charge density and curvature
The surface charge density on a conductor need not be uniform. On an irregularly shaped conductor it is larger where the surface curves more sharply — at pointed regions — and smaller over flatter parts. Since the field just outside is $\sigma/\varepsilon_0$, a high $\sigma$ at a sharp point means an intense field there. This concentration of field at points is the basis of corona discharge and underlies the action of lightning conductors, where a sharp tip ionises the surrounding air. A useful consequence appears when two charged spheres are joined by a wire: equal potential forces a smaller radius to carry a higher surface charge density.
The six results at a glance
| # | Result | Statement | Why |
|---|---|---|---|
| 1 | Field inside | E = 0 everywhere inside the conductor | Free charges drift until the interior field cancels (defining property) |
| 2 | Field at surface — direction | Normal to the surface at every point | Any tangential component would move surface charges |
| 3 | Field at surface — magnitude | E = σ/ε₀, outward for σ > 0 | Gauss's law on a pill box straddling the surface |
| 4 | Excess charge | Resides only on the surface | Zero interior flux ⇒ zero net interior charge (Gauss) |
| 5 | Potential | Constant through the whole volume and on the surface | No work done moving a charge where E = 0 and no tangential E |
| 6 | Cavity / shielding | Field inside an empty cavity is zero | Electrostatic shielding — the Faraday cage; charge stays on the outer surface |
Electrostatics of Conductors in one screen
- In equilibrium the field is zero everywhere inside a conductor — the defining property.
- Just outside, the field is normal to the surface with magnitude $\sigma/\varepsilon_0$; it jumps from $0$ across the surface.
- All excess charge sits on the surface; the interior carries no net charge (Gauss's law).
- The conductor is an equipotential volume — interior and surface at one constant potential; constant $V$ means $\vec E = 0$.
- An empty cavity has zero field — electrostatic shielding (Faraday cage); charge resides on the outer surface.
- Surface charge density is higher where curvature is greater (sharp points), giving intense local fields.