Conductors and Insulators

The broad governing conclusion is that material structure controls the mobility of charge carriers and the response of bound charges. Conductors permit redistribution, induction and effective electrostatic shielding, whereas insulators retain localized charge and can polarise. Hence charge motion, distribution and field response depend on the material. Option B states this complete conclusion. A and C are false generalisations, while D confuses charge behaviour with mass alone.

The governing principle is electrostatic equilibrium in a conductor. A conductor contains mobile free charges, and an electric field exerts force F = qE on each charge. If E were non-zero anywhere inside, those charges would drift and the conductor would not remain at rest. They redistribute on the surface until the internal field becomes zero. Hence A is correct; the other choices make false claims about particles, neutrality, or insulators.

In electrostatic equilibrium, the entire conductor is an equipotential body, so any two internal points must have the same potential. A potential difference means the electric potential varies within the conductor; consequently an electric field exists, since E is related to the spatial rate of change of potential. That field exerts force on free charges and makes them move. Therefore B is correct, while A, C, and D contradict conductor behaviour.

The governing concept is the redistribution of excess charge in a conductor. Like charges repel one another, and the mobile charges can move through the conducting material. They continue rearranging until electrostatic equilibrium is reached, when the electric field inside the conducting material is zero and excess charge resides on the outer surface. Thus C is correct. A is irrelevant, B violates charge conservation, and D falsely describes conductors.

The governing concept is electrostatic induction and the zero electric field inside conducting material. If the charge in the cavity is +q, a Gaussian surface drawn within the conductor must enclose zero net charge, so the inner surface induces −q. This charge is equal in magnitude and opposite in sign; the conductor’s outer surface may carry compensating charge depending on its total charge. Therefore option D is correct, not zero or a partial charge.

Let the charge inside the cavity be −q. Electrostatic equilibrium requires +q on the inner surface, because the electric field within the conductor must be zero. Since the conductor was initially neutral and has not been grounded, its total charge remains zero: (+q) on the inner surface must be balanced by −q on the outer surface. Thus option A is correct; zero would violate charge conservation, while infinity is physically meaningless.

The charge +q inside the cavity still induces −q on the inner surface, because the field inside the conducting material must vanish. However, earthing fixes the conductor’s potential and allows charge to flow between the conductor and Earth. The outer surface therefore need not retain the charge required for an isolated neutral conductor; in the usual symmetric setup it can have zero total charge. Hence option C is correct.

In electrostatic equilibrium, free charges in a conductor must have no net tangential force. If a parallel, or tangential, electric-field component existed at the surface, the force qE_parallel would drive mobile surface charges along the conductor. Their redistribution would continue until that component became zero. The remaining field can be normal to the surface. Therefore option A gives the physical reason; the other choices are unrelated.

At electrostatic equilibrium, the tangential component of the electric field at a conductor’s surface is zero; otherwise free charges would move along the surface. Consequently, the field immediately outside has only the normal component and is perpendicular to the surface. For a positively charged surface it points outward, while for a negatively charged surface it points inward. Thus option C states the direction correctly; it is not generally parallel or irregular.

For a conductor in electrostatic equilibrium, the field just outside the surface is related to the local surface charge density by E_normal = σ/ε₀ in vacuum. Thus a region with larger σ has a stronger nearby normal electric field. This is a local relation, not a property determined by colour, name, or sound. Therefore option B is correct, and the wording ‘local value’ appropriately points to local surface charge density.

A conductor in electrostatic equilibrium can have a nonuniform surface charge distribution. At a sharp tip, the small radius of curvature causes charges to crowd more closely, producing a larger local surface charge density σ. Since the external field near the surface is approximately σ/ε₀, the field becomes stronger there. The conductor does not become an insulator and charge is not destroyed, so option A is correct.

At a sharp metal tip, charge accumulates more densely because the radius of curvature is small. The resulting large local surface charge density produces a strong electric field, approximately E = σ/ε₀ just outside the conductor. If this field is sufficiently high, it can ionise nearby air and start corona or electrical discharge. Thus option C gives the correct chain of reasoning; the other statements contradict conductor physics.

An isolated spherical conductor has complete rotational symmetry: no point on its surface is physically distinguished from another. Mobile charges redistribute until electrostatic equilibrium is reached, and the symmetry then requires the surface charge density to be the same everywhere. The sphere need not be earthed, and a conductor does contain mobile charges; charge resides on the surface rather than only at the centre. Therefore option C is correct.

A conductor contains mobile free charges. When an external charge is brought near it, the electric force is stronger on the nearer side and weaker on the farther side, so charges redistribute over the surface. This is electrostatic induction. The conductor remains a conductor, and its total charge is conserved if it is isolated; only its distribution changes. Therefore option A is correct, while the other options violate basic charge and material principles.

The governing concept is electrostatic induction in a conductor. Free electrons inside the neutral conductor are attracted toward the nearby positive rod, so the near end has an excess of electrons and becomes negatively charged by induction. The far end is left electron-deficient and becomes positive. No net charge is created because the conductor remains isolated; only charge separation occurs. Therefore, option B is correct, while A reverses the induced signs and C and D ignore separation.

The governing principle is electrostatic induction. A negatively charged rod repels the mobile electrons in a nearby neutral conductor. Electrons move toward the far side, leaving an electron deficit at the near side. That deficit is described as a positive induced charge or positive effect. The conductor need not gain a net charge, and the amount is not infinite. Hence option A is correct; B reverses the electron movement, while C and D contradict the physical process.

The governing concept is conservation of charge during electrostatic induction. Bringing a charged body nearby produces redistribution of free charges within the conductor, but there is no physical contact and no conducting path to earth. Thus electrons cannot enter or leave the isolated conductor. If it was initially neutral, the positive and negative induced regions have equal total magnitude, so its net charge remains zero. Option C is correct; A and B confuse local charge separation with net charging, and D is impossible.

The governing concept is charging by induction. A nearby charged body first separates charges in the conductor. Earthing then connects the conductor to Earth, a vast charge reservoir, so electrons can flow into or out of it in response to the external field. After the earth connection is removed in the correct sequence, the conductor retains a net charge. Thus option A is correct; the other choices describe no physical function of earthing.

The governing idea is induction with an earth connection. A positive rod attracts electrons toward the conductor’s near surface, making the conductor electron-deficient unless electrons are supplied. Because the conductor is earthed, electrons can flow from Earth, which acts as a large reservoir, into the conductor. Electrons do not travel from the insulating gap through the rod, and charge is not destroyed. Therefore option B is correct; A gives the opposite direction.

The governing principle is electrostatic induction combined with earthing. A negatively charged rod repels the conductor’s mobile electrons. Since the conductor is connected to Earth, those repelled electrons can leave the conductor and flow into the Earth, a very large reservoir. They cannot normally cross the gap into the rod, and earthing means a path is available, so “nowhere” is incorrect. Hence option B is correct; option A describes the usual direction for a positive external rod.