Conductors and Insulators

At a sharp portion of a conductor, the radius of curvature is small, so surface charge tends to accumulate there. The local surface charge density becomes large, and the nearby electric field, approximately E = σ/ε₀, becomes strong. This strong field helps ionise nearby air and provides a preferred path for charge leakage or discharge. Therefore option A is correct; the other choices contradict electrostatic principles.

In electrostatic equilibrium, the electric field inside the conducting material must be zero; otherwise free charges would continue to move. A charge placed inside the cavity induces an equal and opposite net charge on the cavity’s inner surface, producing a field that cancels the field within the metal. The conductor’s outer surface may carry the remaining charge required by its total charge. Hence option A is correct.

Rubbing transfers electrons between two materials, leaving one surface charged. In a conductor, many mobile electrons move readily, so excess charge redistributes over the surface until electrostatic equilibrium is reached. An insulator has very few mobile charge carriers, so the transferred charge remains near the region where rubbing occurred. Therefore option A is correct; the other options misstate the nature of insulation.

Free charges in a conductor are mobile. If a nonzero net electric field existed within the conducting material, these charges would experience a force and continue to move, so the conductor would not be in electrostatic equilibrium. Charges therefore redistribute mainly on the surfaces until their induced field cancels the external field within the conducting material. Option D is incorrect because zero total electric flux does not imply that the electric field is zero at every point.

The governing concept is electrostatic equilibrium in a conductor. Since the electric field is related to the potential gradient, a nonzero potential difference across an interior region implies a nonzero electric field. That field exerts force qE on mobile charges, causing them to drift until the interior becomes equipotential. Therefore B is correct; sound, insulation, and conversion of charge into mass do not follow from a potential difference.

Free charges can move in a conductor. If the electric field inside the conducting material were nonzero, these charges would experience a force and continue moving, so electrostatic equilibrium would not be possible. At electrostatic equilibrium, the electric field inside the conductor is zero; therefore, the excess charge redistributes to the outer surface. Option B is incorrect because charge is not destroyed; only its distribution changes.

In electrostatic equilibrium, the electric field inside the material of a conductor is zero. Take a Gaussian surface within the conducting material surrounding the cavity. Its electric flux is zero; therefore, by Gauss’s law, the net charge enclosed must be zero. Hence, \(+q+Q_{\text{inner}}=0\), so \(Q_{\text{inner}}=-q\). Option \(0\) is incorrect because it would leave a net enclosed charge \(+q\) for this Gaussian surface.

In electrostatic equilibrium, the electric field within the conducting material is zero. For a Gaussian surface lying in the conductor and enclosing the cavity, the net enclosed charge must be zero. Hence, the total induced charge on the inner surface is −q. Since the conductor was initially neutral and is isolated, its total charge remains zero; therefore, the total charge on its outer surface must be +q. The charge distribution on the outer surface may be non-uniform, but its total is +q. Option B represents the charge on the inner surface, not on the outer surface.

The governing ideas are Gauss’s law, induction, and earthing. A positive charge inside the cavity induces an equal negative charge on the cavity wall so that the electric field inside the conducting material is zero. If the conductor is earthed, charge can flow between it and Earth; the outer surface need not retain a compensating positive charge and can be neutral. Thus B is correct, while A ignores earthing and C and D are physically meaningless.

The governing concept is electrostatic equilibrium of free charges on a conductor. Suppose the external field had a tangential component along the surface. It would exert a tangential force qE_t on mobile surface charges, making them move and rearrange. In equilibrium that component must therefore be zero, leaving only the normal component; the field just outside is perpendicular. Hence A is correct, and the other options contradict basic conductor behaviour.

The governing condition for electrostatic equilibrium is that the tangential component of electric field at a conductor’s surface must be zero. If E_t is nonzero, a surface charge experiences a force qE_t parallel to the surface. Because conductor charges are mobile, they move and redistribute, producing a transient current and destroying the assumed static equilibrium. Therefore B is correct; charges do not vanish and the conductor does not lose its mass.

The governing relation at a conductor surface is E just outside = sigma divided by epsilon_0 in vacuum, where sigma is the local surface charge density. Thus a region with greater charge per unit area generally has a stronger nearby normal electric field, subject to the surrounding medium. Option A is correct. Colour, sound, and the conductor’s name do not determine the electrostatic field and are irrelevant distractors.

In electrostatic equilibrium, the electric field inside a conductor is zero. In vacuum, the normal electric field just outside its surface is determined by the surface charge density: |E_{text{out}}| = |σ|/ε_0. Hence, where |σ| is larger, the magnitude of the external field is also larger. The field is normal outward for positive σ and normal inward for negative σ. The factor 1/2 in option D applies to an isolated uniformly charged non-conducting sheet, not to a conductor.

In electrostatic equilibrium, charge redistributes over a conductor’s surface. At a region with a small radius of curvature, such as a sharp point, the surface charge density is high and the electric field just outside the surface becomes very strong. This strong field can ionise nearby air molecules, initiating corona discharge or leakage of charge. Option B is incorrect because all points of a conductor in equilibrium are at the same potential, even though the electric field near a sharp point is stronger.

With no external electric field or nearby charge, every direction and every point on the surface of a sphere are equivalent. Therefore, in electrostatic equilibrium, the surface charge density \(\sigma\) cannot depend on direction and must be uniform over the surface. Being at one potential is necessary for a conductor in equilibrium, but it alone does not ensure uniform charge density; an irregularly shaped conductor can be equipotential while having non-uniform surface charge density.

The governing concept is electrostatic induction in a conductor. Free electrons can move through the conducting material, so an external charge attracts or repels them more strongly on the nearer side than on the farther side. This redistribution makes surface charge density non-uniform, although the conductor’s total charge need not change. Therefore, option A is correct; the other options contradict the presence of mobile charges and charge conservation.

The positively charged rod attracts the conductor’s free electrons toward the nearer surface. Thus, the nearer surface acquires induced negative charge, while deficiency of electrons leaves induced positive charge on the farther surface. Since the conductor is isolated, no charge is transferred to or from it, so its net charge remains zero. Option B reverses the actual induced-charge distribution.

This is electrostatic induction. A negatively charged rod repels the conductor’s mobile electrons toward its farther end. The near end therefore has an electron deficiency and behaves positively, while the far end has an excess of electrons and behaves negatively. The conductor remains neutral overall because no charge has entered or left. Hence option A is correct; B reverses the electron movement, while C and D ignore charge separation.

The governing principle is conservation of charge for an isolated conductor. A nearby charged rod can produce induction, so positive and negative charges separate locally on different regions. However, because there is no contact and no earth connection, no charge is supplied or removed from the conductor. Its net charge therefore remains zero if it was initially neutral. Option B is correct; the other choices confuse redistribution with net charging.

Charging by induction requires more than merely separating charges. First, the nearby charged body polarises the conductor. Earthing then provides a conducting path through which electrons can enter or leave, depending on the sign of the external charge. After the earth connection is removed, the conductor can retain a net charge. Thus option B states the essential role; the remaining options have no physical connection with induction.