Conductors and Insulators

The governing conclusion is that material structure controls the response of charge. In conductors, mobile carriers permit redistribution, electrostatic shielding, and induction. In insulators, charges are largely bound, so localization and polarisation are more important. Therefore B is the comprehensive statement. A ignores material differences, C reverses the nature of insulators, and D confuses charge with mass.

The governing principle is electrostatic equilibrium: the electric field within the conducting material must be zero. If a charge +q is placed inside a cavity without touching the conductor, Gauss’s law requires an induced charge −q on the cavity’s inner surface so that the enclosed net charge for a Gaussian surface in the metal is zero. Hence A is correct; the induced charge is not positive, and charge is not destroyed.

Let the charge inside the cavity be −q. To keep the electric field zero in the conducting material, electrostatic induction places +q on the inner surface. The conductor as a whole was initially neutral, so its total surface charge must remain zero: (+q)inner + Qouter = 0. Therefore Qouter = −q, an equal negative charge, making option B correct. It is not zero because the inner induced charge must be balanced.

The governing condition applies only to the interior of the conducting material in electrostatic equilibrium, not to all space around it. Excess charge can reside on the surface, and that surface charge produces an electric field outside the conductor. For example, a charged conducting sphere has zero field inside its material but a nonzero external field. Thus B is correct; zero internal field does not imply zero field everywhere.

In electrostatic equilibrium, free charges in a conductor cannot continue moving. If the electric field had a tangential component along the surface, it would exert a force on surface charges and produce motion. Therefore that tangential component must be zero, leaving only the normal component outside the surface. Thus option A is correct. The other options incorrectly deny surface charge or misunderstand the location of the field.

Excess charge on an isolated conductor resides on its outer surface and redistributes until electrostatic equilibrium is reached. The local surface charge density is not generally uniform when curvature changes: sharper regions require a greater concentration of charge and consequently have a stronger nearby electric field. Therefore option A is correct. The other options deny mobile charge or introduce irrelevant colour and centre-based ideas.

At electrostatic equilibrium, charge density tends to become larger at a sharply curved or pointed part of a conductor. Since the field just outside is related to surface charge density by E = σ/ε₀, a larger σ produces a stronger local electric field. If this field is sufficiently high, it can accelerate electrons and ionise air molecules. Hence A is correct; the other choices have no physical basis.

A charged isolated sphere has the same geometrical environment in every direction. Electrostatic equilibrium and spherical symmetry therefore require the surface charge density to be uniform at corresponding points. An irregular conductor has regions with different curvatures, so charge density can vary, usually becoming larger near sharper parts. Thus option A is correct; earthing is not required, and charge is not destroyed.

A conductor contains mobile free electrons. When an external charge approaches, its electric field exerts forces on these electrons, causing them to move over the conductor's surface until electrostatic equilibrium is restored. This separation is electrostatic induction; the conductor's net charge remains unchanged if it is isolated. Therefore A is correct, while the other options incorrectly claim insulation, destruction, or a colour change.

A positively charged rod attracts the conductor's mobile electrons. Electrons shift toward the near end, leaving the far end with an electron deficit and therefore an induced positive charge. The conductor as a whole remains neutral because no charge has entered or left; only separation has occurred. Thus option A is correct. Protons do not freely flow through the solid conductor, and earthing is not assumed.

The negatively charged rod repels the conductor's mobile electrons. These electrons move toward the far end, producing an excess of negative charge there, while the near end becomes relatively positive because it has lost electrons. Since the conductor is isolated, its total charge remains zero; only redistribution occurs. Therefore A is correct. Protons do not move freely, and no earthing is stated.

An external charge can exert forces on the conductor's free electrons and separate positive and negative regions. However, when there is no physical contact and no conducting path to Earth, electrons cannot enter or leave the conductor. Consequently, the algebraic sum of charge remains zero for an initially neutral conductor, although local surface charge densities change. Hence A is correct; induction changes distribution, not net charge.

In charging by induction, the external charged body first separates charges in the conductor. While earthing is connected, electrons can still flow between Earth and the conductor in response to the external field. Removing the earth connection first isolates the conductor and traps the acquired net charge. Only after that should the external body be removed, allowing the charge to spread over the conductor. Thus A is correct.

A positively charged rod creates an electric field that attracts electrons toward the nearby conductor. If the conductor is earthed, Earth acts as a vast reservoir of mobile charge and provides a conducting path. Electrons therefore flow from Earth into the conductor until the electrostatic condition is established. The rod does not create or destroy electrons, and the conductor remains a conductor. Hence A is correct.

The governing concept is electrostatic induction in a conductor. A negatively charged rod repels the conductor’s mobile electrons, pushing them toward the side connected to Earth. Because earthing provides a conducting path to the huge charge reservoir of Earth, these electrons can flow away until the potential condition is established. Thus A is correct; the rod repels electrons, does not pull protons, and conductors do contain mobile electrons.

Polarisation separates positive and negative bound charges slightly inside an initially neutral insulator, so its net charge can remain zero. If an external charged body is nearby, the oppositely charged side is closer than the similarly charged side. Since electrostatic force varies as 1/r², the nearer attraction is stronger than the farther repulsion, producing a net attraction. Hence A is correct.

The microscopic distinction depends on the mobility of charge carriers. In a conductor, electrons are sufficiently free to redistribute over a macroscopic distance when an external electric field is applied; this is electrostatic induction. In an insulator, electrons remain bound to atoms or molecules and shift only slightly, creating polarisation. Therefore A is correct; neither process requires proton motion or a necessary change in net charge.

A conductor becomes equipotential in electrostatic equilibrium because its free charges redistribute until no tangential electric field remains. The wrong assumption is that an insulator has the same freely mobile charge carriers. In an insulator, charges are mainly bound and cannot move over large distances, so its surface need not become equipotential. Hence A is correct; mass, shape, and molecular structure are not the mistaken assumptions described.

When two conducting spheres touch, mobile charges flow between them until both reach the same electric potential. If the spheres are identical in size and material, their capacitances are equal; equal potential then requires equal final charges, because q = CV. Thus A is correct. Charge is conserved during the redistribution, and neither insulation nor zero gravity is needed for equal sharing.

The governing concept is electrostatic equilibrium: when two conductors touch, charge flows until their potentials become equal, not until their charges become equal. Since the relation is Q = CV, different-sized conductors generally have different capacitances C. At the same potential V, their charges Q can therefore be unequal. Options B and C incorrectly claim that charge stays on only one conductor, while D is not generally true.

The zero-field condition inside a conductor in electrostatic equilibrium means that mobile charges have rearranged until the net force is zero. It does not mean that the conductor has no charge: any excess charge resides on its outer surface, and the potential is constant throughout the conductor because E = −dV/dr = 0. Thus A is the incorrect conclusion; B, C, and D are valid consequences or compatible statements.

In a conductor, free charges can move. If excess charge remained in the bulk at electrostatic equilibrium, it would produce an internal electric field and continue pushing charges, contradicting equilibrium. The charges therefore redistribute until the field inside is zero; excess charge is then located on the surface. This is a rearrangement, not creation or destruction of charge. Hence A correctly explains the phenomenon, while B, C, and D are physically incorrect.

Free charges in a conductor move whenever a net electric force acts on them. Their rearrangement stops in electrostatic equilibrium, when the internal electric field and hence the net force on each mobile charge are zero. The conductor is then an equipotential body. Charges do not necessarily collect at the centre, nor do they change into mass; a colour change has no relation to electrostatic equilibrium. Therefore A is correct.

The electromagnetic energy density of an electrostatic field in vacuum is u = ½ε₀E², and in a material it is similarly proportional to E². Therefore, if the electric field inside the conducting enclosure is exactly zero, the energy density associated with that field is zero, so the total field energy in that region is taken as zero. This does not claim that every form of energy disappears. Hence A is correct; B, C, and D do not follow.

This is electrostatic shielding. When an external electric field is applied to a conducting cage, its mobile electrons redistribute over the outer surface. The induced surface-charge distribution produces a field that opposes the applied field within the enclosed region; in an ideal closed conductor, the net internal field is zero. The metal does not block gravity or destroy charge, and light-to-charge conversion is irrelevant. Thus A is correct.