Conductors and Insulators

Free charges in a conductor can move. If an electric field existed inside the conductor, it would exert a force on these charges and keep them moving. Therefore, in electrostatic equilibrium, the electric field inside the conductor must be zero. Charges redistribute until this condition is reached, leaving the excess charge on the outer surface. Option D is incorrect because electric force does act on free charges before equilibrium; it becomes zero only after the internal electric field becomes zero.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.