Conductors and Insulators

The positively charged rod attracts the conductor’s free electrons, making the side nearer the rod negative and the farther side positive. This is only a redistribution of charge. Since the conductor is isolated and is neither touched nor grounded, no charge enters or leaves it; therefore, its net charge remains zero. Distance may affect the extent of charge separation, but not the net charge.

A is correct. Bringing a charged object near the conductor separates charges within it. When the conductor is earthed, electrons flow between the conductor and Earth. Disconnecting the earth connection while the charged object is still nearby leaves a net charge on the conductor. After the charged object is removed, this charge remains, with a sign opposite to that of the inducing charge. In option B, there is only temporary charge separation; without earthing, no net charge remains on the conductor.

Metals have low electrical resistance, so they allow electric current to flow easily and are suitable for the core of a wire. Rubber has very high resistance, so it acts as an insulator and reduces the chance of current reaching the user and causing an electric shock. In option A, these properties are reversed.

Rubber is an insulator, so it has very few free charge carriers and offers high resistance to electric current. This reduces the chance of current flowing through the body. In contrast, metal is a conductor with free electrons, so metal gloves can provide an easy path for current.

Normal air has very few mobile charge carriers, so it behaves as an insulator. During lightning, an extremely strong electric field ionises air molecules, creating free electrons and positive ions. These charge carriers provide a path for electric current. Option B is incorrect because air does not become a metal; it becomes temporarily conducting due to ionisation.

Metal spheres are conductors, so free charge flows on contact until both spheres reach the same potential. Since the spheres are identical, equal potential corresponds to equal charge on them. With no external influence, total charge is conserved; therefore, after separation each sphere has half of the initial total charge. Option D includes equal sharing but is incorrect because total charge cannot increase.

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 contains many mobile charge carriers and has low electrical resistivity, so it allows current to pass efficiently and is commonly used as the conducting core of a wire. Therefore option A is the correct application. Rubber, glass and plastic are generally insulators; they are useful for protection and insulation rather than for carrying the main current or increasing it. The option refers to copper as the conducting part, not its outer covering.

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.