Conductors and insulators

This topic belongs to Unit I (Electrostatics), inside the CBSE Class 12 Physics chapter "Electric Charges and Fields," following directly on the basic properties of charge — additivity, conservation, and quantisation ($q = ne$). The prescribed treatment is qualitative: describe, in words and simple pictures, why metals conduct and insulators do not, and connect this to how charging by conduction and induction actually happens on real objects such as spheres and rods. No formal proof involving Gauss's theorem is expected at this stage (that machinery is applied later in the same chapter to symmetric charge distributions); here the goal is purely the physical vocabulary of free versus bound charge that the rest of electrostatics — and, later, capacitors — leans on.

Every solid is built from atoms, each with a positively charged nucleus surrounded by electrons. What separates a conductor from an insulator is not the total number of electrons present but how tightly the outermost ones are held. In a metal such as copper, silver, or aluminium, the outermost (valence) electrons are so weakly bound that they detach from their individual atoms altogether and wander freely through the entire crystal — a picture often called the "electron sea" or "free-electron gas." In glass, rubber, or dry wood, by contrast, every electron remains attached to its own atom or molecule; there is no sea to speak of, only tightly held individual charges. Because a conductor's electrons are mobile, any electric field applied inside it pushes them until they pile up on surfaces in just the right pattern to cancel that field completely in the interior. This is the defining property of a conductor in electrostatic equilibrium:

where: $\vec E_{\text{inside}}$ is the net electric field anywhere inside the bulk of the conducting material, once the free charges have finished rearranging themselves (electrostatic equilibrium — no further net motion of charge). Physically this says a conductor "shields" its own interior: however strong the external field or however much charge sits on its surface, an observer drilled a tiny cavity into the metal and standing inside would measure zero field, because the mobile electrons have already arranged themselves to cancel any field that would otherwise exist there. A second consequence follows immediately: since $\vec E_{\text{inside}} = 0$ everywhere in the bulk, no work is done moving a test charge from one interior point to another, so every point inside a conductor — and every point on its surface — sits at the same electric potential. A conductor in electrostatic equilibrium is therefore an equipotential body, and its outer surface is an equipotential surface. This equipotential property, together with the requirement of zero internal field, is exactly what forces excess charge on an isolated conductor to reside entirely on its outer surface rather than anywhere in its interior — any charge sitting inside the bulk would create a field there, which contradicts equilibrium.

Conductors are dominated by their sea of free electrons. In a typical metal there is roughly one free electron per atom (sometimes more), and these electrons are in constant, rapid thermal motion, colliding with the fixed lattice of positive ions but never trapped by any single one. Because of this mobility, a conductor responds to any nearby charge or applied field almost instantaneously (on the scale of everyday timekeeping): the free electrons rearrange in a fraction of a second to reach equilibrium. Common conductors include all metals, the human body (because of dissolved ions in body fluids), and moist earth.

Insulators (dielectrics) hold every electron in a tight orbital bond to a specific atom or molecule. There is no free-electron sea; the material offers essentially no pathway for charge to travel any macroscopic distance. Rubbing an insulator such as glass, ebonite, or a plastic comb can still displace charge locally — friction strips a few electrons off one surface and deposits them on another — but once deposited, that charge has nowhere to go, and it stays put until it slowly leaks away (often via moisture in the air) or is deliberately removed.

Semiconductors, such as silicon and germanium, are intermediate: they possess a small, thermally activated population of mobile charge carriers — far fewer than a metal, but a nonzero number, unlike a true insulator. Their conductivity therefore sits between the two extremes and, notably, tends to increase with temperature (more thermal energy frees more carriers), the opposite of the metallic trend. The full physics of how this works belongs to a later chapter on semiconductor electronics; here it is enough to place semiconductors correctly on the conductor–insulator spectrum.

Conduction is charging by direct contact. When a charged conductor touches a neutral (or oppositely/differently charged) conductor, free electrons flow across the point of contact — from the region of higher electron concentration to lower — until both bodies reach the same electrostatic potential. If the two conductors are identical in size and shape, symmetry makes the final total charge split equally between them once contact is broken. Because charge is conserved throughout, the total charge before contact always equals the total charge after — it is only the distribution between the two bodies that changes.

Induction is a subtler process: a charged rod is brought near a neutral conductor, without touching it. The rod's field pulls the conductor's free electrons toward (or pushes them away from) the near side, so the near face acquires a charge opposite to the rod's and the far face acquires charge of the same sign as the rod's — yet the conductor's total charge remains exactly zero throughout, because nothing has been added or removed, only separated. This is why an induced conductor can attract a nearby charged rod even while carrying zero net charge overall: the near, opposite-sign face is closer and dominates. If the induced charge is to be made permanent, the conductor must be momentarily earthed while the inducing rod is still present, letting one sign of charge escape to the ground; removing the earth connection and then the rod leaves the conductor with a net charge of the sign originally repelled.

Earthing (grounding) exploits the fact that the earth itself, being enormous, behaves as an essentially infinite reservoir of charge at zero (reference) potential. Connecting a charged conductor to the earth by a conducting wire lets excess charge flow to or from that reservoir until the conductor's potential matches the earth's, which for a small conductor connected to something as vast as the planet effectively means it ends up neutral. This is why touching a charged conductor with your (conducting) hand, while you are in contact with the ground, discharges it — and why lightning rods, appliance earth wires, and static-discharge straps all work on exactly this principle.

Board level - induced charge separation on a metal sphere

A neutral, isolated metal sphere on an insulating stand is brought near a positively charged rod, without touching it. Describe what happens to the charge distribution on the sphere, and explain why the same thing could not happen if the sphere were made of glass.

Step 1. The metal sphere is a conductor, so it contains free electrons that can move throughout its entire body in response to any applied field.

Step 2. The positive rod's field attracts these free electrons toward the near side (the side facing the rod), leaving that near face negatively charged, while the far side is correspondingly left short of electrons and becomes positively charged. This is electrostatic induction; the sphere's total charge stays exactly zero throughout, since only a redistribution has occurred, not a creation of charge.

Step 3. If the sphere were made of glass instead, its electrons are bound to individual atoms and cannot migrate through the material. No large-scale charge separation can occur; at most, the molecules directly facing the rod undergo a slight, localised polarisation, with essentially no effect at the far side.

Answer: the metal sphere shows a clear induced charge separation — the near face negative, the far face positive, total charge still zero — because free electrons migrate through the conductor; a glass sphere cannot show this because its electrons remain bound to their parent atoms.

Competitive level - charge sharing between unequal, then repeated, conducting spheres

Two identical isolated metal spheres, A with charge $+12\ \text{nC}$ and B with charge $-4\ \text{nC}$, are brought into contact and separated. A third identical, initially neutral sphere C is then brought into contact with sphere A alone and separated. Find the final charge on all three spheres.

Step 1. When A and B (both conductors) touch, free charge flows across the contact until the combined system reaches a common electrostatic equilibrium. Total charge is conserved: $q_{\text{total}} = (+12) + (-4) = +8\ \text{nC}$.

Step 2. Because A and B are identical in size and shape, symmetry forces the charge to split equally between them on separation: each ends up with $q_A = q_B = \dfrac{8}{2} = +4\ \text{nC}$.

Step 3. Sphere C, initially neutral, is now touched to sphere A (which carries $+4\ \text{nC}$) alone. The same reasoning applies to this new pair: total charge on A and C together is $(+4) + 0 = +4\ \text{nC}$, and since A and C are identical, it splits equally: $q_A = q_C = \dfrac{4}{2} = +2\ \text{nC}$.

Step 4. Sphere B was not touched a second time, so it retains its charge from Step 2.

Answer: after both contacts, $q_A = +2\ \text{nC}$, $q_B = +4\ \text{nC}$, $q_C = +2\ \text{nC}$ — total still $+8\ \text{nC}$, confirming conservation of charge throughout. Timing note: in a multi-step charge-sharing problem, resolve one contact completely (apply conservation, then split equally for identical conductors) before moving to the next contact — do not average across all three spheres at once unless all three touch simultaneously, which is a different (and rarer) setup.

• Assuming insulators cannot be charged at all — they can be charged (e.g. rubbing a glass rod with silk), but the charge stays localised near where it was deposited rather than spreading over the whole body.
• Thinking induction requires the charged and neutral bodies to touch — induction is specifically the redistribution of charge on a conductor caused by a nearby charged body, with no contact at all.
• Forgetting that an isolated conductor's excess charge always resides on its outer surface, never in the bulk, once electrostatic equilibrium is reached.
• Believing $\vec E_{\text{inside}} = 0$ means "no charge is present inside a conductor at equilibrium" is somehow special to spheres — it holds for a conductor of any shape, in equilibrium, as a direct consequence of free-electron mobility, not sphere geometry.
• Confusing "neutral" with "no charge present anywhere" — an induced conductor with zero net charge still has separated positive and negative regions on its surface; only the total charge is zero, not the local charge everywhere.
• Splitting charge equally between two conductors that touch even when they are of different sizes or shapes — equal splitting only applies to identical conductors; for unequal conductors the final charges depend on their capacitance and only the total charge is guaranteed conserved.

• Explain the difference between conductors, insulators, and semiconductors in terms of free versus bound charge carriers.
• State and justify why the electric field inside a conductor is zero, and why an isolated conductor's surface is an equipotential.
• Explain why excess charge on an isolated conductor always ends up entirely on its outer surface.
• Describe electrostatic induction on a conductor and explain why the total charge stays zero throughout the process.
• Distinguish charging by conduction from charging by induction, and explain how earthing removes charge to the earth's reservoir.
• Solve multi-step charge-sharing problems between identical conductors using conservation of charge and symmetric splitting.

Ask the tutor: want to work through how a charged conductor with a cavity behaves, or get more practice with multi-sphere charge-sharing chains — ask the AI tutor to run one with you step by step.