Conductors and Insulators

Correct answer: C. Tightly bound charge carriers

Explanation: In an insulator, electrons and other charge carriers are tightly bound to atoms or molecules, so they cannot move freely through the material over large distances. Therefore, an excess charge remains localized near where it is deposited. In contrast, charge can spread easily in a conductor because it has free electrons.

Correct answer: D. Because a tangential component would move free charges along the surface, and they would redistribute until it becomes zero

Explanation: In electrostatic equilibrium, the free charges in a conductor are at rest. If a tangential component of electric field existed at the surface, it would exert a force along the surface and move the free charges. The charges redistribute until the tangential component becomes zero. This differs from the normal component, which need not be zero just outside the surface.

Correct answer: A. The total negative charge of the free electrons equals the total positive charge of the metal ions.

Explanation: In a metal, some electrons are free to move, while the positive metal ions remain nearly fixed in the lattice. In the normal state, the total negative charge of the free electrons equals the total positive charge of the metal ions. Therefore, the net charge of the metal is zero, so it is neutral. The mobility of free electrons does not mean that the metal must have a net negative charge; neutrality depends on the balance of total charges.

Correct answer: B. Leakage of charge from the sphere to Earth is greatly reduced

Explanation: A metal sphere is a conductor, so its charge can flow to Earth if it gets a conducting path to ground. An insulating stand has very high resistance, greatly reducing leakage of charge to Earth through the support and helping the sphere retain its charge. The stand does not make the metal sphere an insulator.

Correct answer: C. Negative charge will be induced

Explanation: A positively charged object attracts the free electrons in the conductor. Hence, electrons accumulate at the nearer end, inducing a negative charge there. This is electrostatic induction. Since the conductor is isolated, its net charge remains zero; an equal positive charge appears at the farther end.

Correct answer: D. Away from the charged object

Explanation: A negatively charged object repels other negative charges. In a neutral conductor, electrons are mobile, so they shift away from the nearby negative object. This separation is electrostatic induction: the near side becomes relatively positive and the far side relatively negative, while the conductor remains neutral overall if it is isolated. Thus option D is correct; electrons are neither destroyed nor fixed only at the centre.

Correct answer: A. Because the electric field of the charged object redistributes the free charges in the conductor without contact.

Explanation: When a charged object is brought near a conductor, its electric field redistributes the conductor's free electrons or charges, so contact between the two objects is unnecessary. If the conductor is grounded, charges can flow to or from Earth; after removing the ground connection and then the charged object in the proper order, the conductor is left with a net charge. In contrast, charging by contact requires touching for charge transfer.

Correct answer: A. In contact charging, charge is transferred through physical contact, whereas in induction charging, charges are separated without contact and the object is charged through earthing.

Explanation: In charging by contact, a charged object touches the conductor, so electrons are actually transferred and charge is redistributed between the objects. In charging by induction, bringing a charged object near a conductor without touching it first separates charges in the conductor. Earthing then allows electrons to flow to or from the Earth; after the earth connection is removed, the conductor is left with a net charge. Charge separation alone is polarization, not permanent charging by induction.

Correct answer: C. The centres of bound positive and negative charges undergo a slight relative displacement

Explanation: In an insulator, charges are not free to move through the material over large distances. An external electric field causes a small relative displacement between the centres of bound positive and negative charges in atoms or molecules, producing induced dipoles. Option A describes the motion of free charges in a conductor, not polarisation in an insulator.

Correct answer: D. In an external electric field, free charges redistribute in a conductor, whereas the centres of bound charges shift slightly in an insulator.

Explanation: When an external electric field is applied, free electrons or other mobile charges in a conductor can redistribute easily. This produces separation of induced positive and negative charges on different parts of the conductor; charge is not destroyed. In an insulator, charges remain bound to atoms or molecules, so they do not flow through the material. A slight displacement of the positive and negative charge centres, or alignment of permanent dipoles, produces polarisation. Therefore, D is correct, whereas C incorrectly describes free-charge flow in an insulator.

Correct answer: A. At electrostatic equilibrium, induced charges redistribute on the outer surface and cancel the external field inside the cavity

Explanation: A closed conductor contains mobile charges. When an external electrostatic field is applied, these charges redistribute on the outer surface so that, at electrostatic equilibrium, the electric field in the cavity due to external sources is zero. This is called electrostatic shielding. Option B is incorrect because the conductor does not absorb the field; induced surface charges cancel it.

Correct answer: D. Free charges redistribute on the surface and produce an induced field that cancels the internal field

Explanation: In electrostatic equilibrium, free electrons in a conductor move until their redistribution on the surface produces an electric field that cancels the external field inside the conductor. Therefore, the net electric field inside is zero. Option C is incorrect because a conductor does contain free charges; their redistribution is what produces shielding.

Correct answer: A. The pointed part has a smaller radius of curvature.

Explanation: In electrostatic equilibrium, charge is not distributed uniformly over a conductor’s surface. A region with a smaller radius of curvature, that is, a sharper region, has a stronger electric field near it. Since \(\sigma=\varepsilon_0 E\), the surface charge density \(\sigma\) is greater there. Option B is incorrect because the electric field is zero inside a conductor, whereas just outside a sharp point it is large.

Correct answer: B. Because the surface charge density can be higher at the pointed tip

Explanation: In electrostatic equilibrium, the magnitude of the electric field just outside a conductor is \(E=\sigma/\varepsilon_0\). The surface charge density \(\sigma\) can be higher at a pointed region, so the electric field just outside it is stronger. Contrary to option C, the metal remains a conductor at the pointed tip.

Correct answer: C. It becomes zero because free charges redistribute and cancel the external field inside.

Explanation: Metals contain free electrons. When an external electrostatic field is applied, these charges redistribute until electrostatic equilibrium is reached. In this state, the electric field inside the cavity of a closed conductor due to external sources is zero; this is called electrostatic shielding. Option B is incorrect because metals do have free electrons, whereas charges do not redistribute easily in insulators.

Correct answer: D. Charge flows between the conductor and the Earth until their potentials become equal

Explanation: When the conductor is connected to the Earth, the wire provides a path for charge flow. If there is a potential difference between the conductor and the Earth, electrons flow either to the Earth or from the Earth to the conductor until the conductor reaches Earth potential. Since Earth is a very large charge reservoir, the conductor’s charge does not necessarily remain unchanged.

Correct answer: A. They will redistribute until the electric field and potential difference within the conducting material become zero.

Explanation: A potential difference within a conductor implies an electric field, which exerts a force on free charges. The charges therefore redistribute. In electrostatic equilibrium, redistribution stops only when the electric field inside the conducting material becomes zero; hence the conductor’s interior is equipotential and the potential difference between any two interior points is zero. Option B is incorrect because the conductor’s potential is constant, but it need not be zero.

Correct answer: B. Because the electric field inside the conductor is zero, so the potential difference between any two of its points is zero

Explanation: In electrostatic equilibrium, free charges redistribute until the electric field inside the conductor becomes zero. Since the potential difference is  ext{Δ}V=- extstylerac{}{} ext{∫} ext{}  extbf{E} ext{·d} extbf{l}, a zero electric field gives zero potential difference between any two points of the conductor. Hence, the conductor is equipotential. Option D is incorrect because the field is not merely constant; it is zero in equilibrium.

Correct answer: C. Because free charges do not move far easily in it

Explanation: An equipotential conductor is established when mobile charges redistribute until the internal electric field becomes zero. In an insulator, electrons are strongly bound to atoms or molecules, so charge cannot freely move through the material to cancel field differences. Hence option C is correct. An insulator can possess charge, and its physical state or gravity is unrelated to the equipotential condition, so A, B and D are invalid.

Correct answer: A. Zero

Explanation: 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.

Correct answer: A. Bring a charged object near the conductor, earth the conductor, remove the earth connection while the charged object is still nearby, and then remove the charged object.

Explanation: 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.

Correct answer: C. Low resistance of metal and high resistance of rubber

Explanation: 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.

Correct answer: A. Because rubber resists the flow of electric current, whereas metal allows current to flow easily.

Explanation: 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.

Correct answer: A. A strong electric field ionises air, producing free electrons and ions.

Explanation: 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.

Correct answer: C. The total charge will be conserved, and after separation each sphere will have half of the initial total charge.

Explanation: 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.