Conductors and Insulators

In electrostatic equilibrium, the net electric field within the conducting material is \(\vec{E}_{\text{net}}=0\). The net electric force on a charge \(q\) is \(\vec{F}_{\text{net}}=q\vec{E}_{\text{net}}\), so \(\vec{F}_{\text{net}}=0\). Surface or induced charges may exert individual forces, but their resultant force is zero; therefore, option C is incorrect.

The relation between electric field and potential is E = −dV/dr. If the electric field inside a conductor in electrostatic equilibrium is zero, the potential does not change from one point to another within that conductor. Therefore the potential difference between any two interior points is zero, so option A is correct. A high, infinite or always-negative difference would require a potential variation and a corresponding electric field.

Charges in an insulator cannot flow freely, but an external electric field slightly displaces or reorients its bound positive and negative charges. This is called polarisation. The insulator remains neutral overall, but opposite charge is induced on the surface nearer to the charged object. Since this opposite charge is closer, its attraction is stronger than the repulsion from the like charge on the farther side, giving a net attraction. Unlike option B, charges in an insulator do not become freely mobile as they do in a conductor.

A metal contains free electrons. The electric field of the positively charged rod attracts these electrons toward the rod, so they accumulate on the nearer side of the sphere. Thus, the nearer side becomes negative and the farther side becomes positive because of an electron deficit. This is electrostatic induction. The sphere still has zero net charge; option B reverses the direction of electron motion.

When the conductor is earthed, charge can flow between the conductor and the Earth until their potentials become equal. Because the Earth is very large, its potential is treated as nearly unchanged and is conventionally taken as zero. Therefore, the conductor reaches the Earth's potential; it need not become specifically positive or negative.

Free charges can move easily in a metal. If the person touching the object is connected to Earth, the body provides a conducting path between the object and Earth. For a negatively charged object, excess electrons may flow to Earth; for a positively charged object, electrons may flow from Earth to the object. Thus, the object's net charge can decrease. Option B is incorrect because a hand does not permanently stop the metal's free electrons.

In electrostatic equilibrium, the electric field inside a conductor is zero and excess charge resides on its outer surface. A change in surface curvature changes the surface charge density; regions that are sharper, or have a smaller radius of curvature, generally have greater charge density and a stronger electric field. Therefore, option A is correct. Option C is incorrect because excess charge is on the conductor’s surface, not at its centre.

In electrostatic equilibrium, excess charge resides on the outer surface of a conductor. Just outside the surface, \(E=\sigma/\varepsilon_0\). Near pointed or highly curved regions of an irregular conductor, the electric field is stronger; hence the surface charge density \(\sigma\) is greater there. In contrast, symmetry makes the surface charge density uniform on a uniformly charged spherical conductor.

In electrostatic equilibrium, the electric field inside a conductor is zero. If an electric field remained inside, free charges would experience a force and continue to redistribute, so equilibrium would not exist. After redistribution, there is no net drift of free charges, and excess charge resides on the conductor’s surface. Option C correctly states that the internal field is zero but incorrectly places excess charge throughout the volume.

A conductor contains free electrons. If the electric field
\(E\) inside it is non-zero, every free charge experiences a force
\(F=qE\). The charges therefore move and redistribute, so electrostatic equilibrium cannot exist. Equilibrium is reached only when this redistribution makes the electric field inside the conductor zero; hence option B is incorrect.

In electrostatic equilibrium, the electric field inside the conducting material is zero. Therefore, the potential difference between any two points is
0, so the conductor is an equipotential body and the potential is the same at all points. The potential itself need not be zero; its value depends on the chosen reference.

A conductor contains free or mobile charge carriers. When an external electric field is applied, these charges redistribute, and at electrostatic equilibrium the electric field inside the conductor becomes zero. In an insulator, charge carriers are mostly bound to atoms or molecules; they do not move freely through the material as in a conductor, but undergo small displacements that produce polarization. Therefore, option A is correct. Option B reverses the properties of conductors and insulators.

Copper is a conductor with low resistivity, so it is used as the inner core to allow current to flow easily. Rubber has very high resistivity, so an outer rubber covering prevents the user from coming into contact with current. In option C, the outer aluminium covering is also conducting and therefore is not suitable for electrical safety.

Rubbing can transfer electrons and charge the plastic comb. The paper is initially neutral, but the comb's electric field slightly separates charge within it, producing polarisation. Opposite charge is effectively induced on the side nearer the comb, and because it is closer, its attractive force is stronger than the repulsion from the farther like charge. Hence the paper is attracted to the comb.

In electrostatic equilibrium, free charges in the conductor redistribute so that the electric field within the conducting material is zero. If the closed cavity contains no charge, its inner surface is an equipotential surface, and the electric field throughout the cavity is also zero. Thus, an external electrostatic field does not penetrate the cavity; this is electrostatic shielding. Option A is incorrect because charge redistribution on the conductor cancels the effect of the external field inside the cavity.

In electrostatic equilibrium, the electric field within the conducting material is zero. If excess charge remained in the interior volume, it would produce an internal electric field and charges would continue to move until equilibrium was reached. Therefore, excess charge resides on the outer surface, not throughout the volume or at the centre.

In an insulator, electrons and positive charges are generally bound to atoms or molecules. When an external electric field is applied, these bound charges shift by very small amounts in opposite directions, producing electric dipoles. This process is called dielectric polarisation. Since charges do not move freely through the material, no sustained current flows. In contrast, conduction involves the bulk motion of free charges.

The negatively charged object repels the conductor’s free electrons toward the far side. When the conductor is earthed, these electrons flow to Earth. If the earth connection is removed before the nearby object is taken away, the electrons cannot return; the conductor is left with a deficiency of electrons and hence becomes positively charged. This is charging by induction; charging by conduction would require direct contact between the charged object and the conductor.

Rubbing can transfer electrons from one material to another, thereby charging an object. In an insulator, electrons are tightly bound to atoms or molecules, so there are very few freely mobile charge carriers. Hence, the transferred charge remains localized near the rubbed region. In contrast, free electrons in a conductor allow charge to spread relatively quickly.

The key difference is the mobility of charge carriers. In a conductor, free electrons can move through the material and redistribute charge, usually placing excess charge on the surface in electrostatic equilibrium. In an insulator, charges are mainly bound to atoms or molecules and remain localized, with only limited polarization. Thus option A gives the governing reason; colour, shape, mass and sound do not determine this distribution.

In electrostatic equilibrium, free charges redistribute until the electric field within the conducting material becomes zero. If a non-zero field existed inside, it would exert a force on free charges and they would continue to move, so equilibrium would not be possible. Even a uniform non-zero field as stated in option B would cause charge motion.

Electrostatics distinguishes materials by how easily their charge carriers move. In conductors, mobile electrons redistribute charge rapidly, whereas in insulators charges remain largely bound and may only shift slightly during polarization. This proves that material nature affects charge motion and distribution, so option A is correct. Colour has no governing role, materials do not conduct equally, and electric fields arise from charge rather than only from mass.

In electrostatic equilibrium, free charges in the conductor rearrange to oppose the external electric field. Since there is no charge in the cavity of the closed conductor, the cavity boundary is an equipotential surface and the resultant electric field inside the cavity is zero. Thus, the external field does not penetrate the cavity. Unlike option B, no non-zero uniform field is produced inside the cavity.

A tangential electric field exerts a force parallel to the conductor’s surface on free charges, so they begin to move. The charges redistribute until electrostatic equilibrium is established. In electrostatic equilibrium, the tangential component of electric field at a conductor’s surface is zero and the surface is equipotential. Thus, option D is not true initially; it describes the situation after equilibrium has been reached.

Free charges in a metal can move. They redistribute until electrostatic equilibrium is reached, making the electric field inside the conductor zero. Therefore, the excess positive charge on an isolated metal sphere resides on its outer surface. Option C is incorrect because excess static charge does not remain distributed throughout the volume of a conductor.