Conductors and Insulators

At a sharp tip of a charged conductor, the surface charge density is relatively high. Therefore, the electric field near the tip can become very strong. This strong field can ionise nearby air molecules; the air begins to conduct, so corona or electric discharge may occur. Unlike option B, the electric field at a sharp tip is not zero; it is generally stronger.

In electrostatic equilibrium, free charges redistribute so that the electric field within the conducting material is zero. The inner surface of the cavity is an equipotential surface. Since there is no charge in the cavity, the potential throughout it is constant, so the electric field in the cavity is zero. Grounding is not required; therefore, option D is incorrect.

In a closed conducting enclosure, free charges redistribute in response to an external electric field. In electrostatic equilibrium, the induced charges produce a field that makes the electric field inside the enclosure zero. Thus, the devices are shielded from external electrostatic fields; the enclosure is not primarily used to block light or increase the device's mass.

Option A is correct. When a charged object is brought near the neutral conducting sphere, charges in the sphere separate. Grounding allows electrons to flow between the earth and the sphere. Disconnecting the earth connection while the charged object is still nearby leaves a net charge on the sphere; after the charged object is removed, that charge spreads over the sphere. The final charge on the sphere is opposite in sign to that of the inducing object. In option B, the inducing object is removed before the earth connection is broken, so the sphere becomes neutral again.

When a charged object is brought near a conductor, its electric field redistributes the conductor’s free charges. If the conductor is then grounded, electrons can flow either from Earth to the conductor or from the conductor to Earth. Removing the ground connection first and then removing the charged object leaves the conductor with a net charge, usually opposite to that of the inducing object. Thus, direct contact with the charged object is not required; direct contact is required in charging by conduction.

In electrostatic induction, the conductor’s free charges only redistribute: excess electrons make one side negative, while a deficiency of electrons makes the other side positive. Since the conductor is isolated and no charge enters or leaves it, its total charge cannot change. It was initially neutral, so its net charge remains zero. A positive or negative net charge could result only if the conductor were grounded or charge were transferred to or from it.

In contact charging, the charged body touches the conductor, so electrons or charge are transferred directly. In induction, bringing a charged body near the conductor redistributes charges within it without contact. To leave the conductor with a permanent net charge, it is usually earthed; the conductor then retains a charge opposite in type to the inducing body. Unlike option D, no direct charge transfer from the inducing body occurs in induction.

Electric force is given by \(\vec{F}=q\vec{E}\). Since \(\vec{E}=0\) inside the conductor, for any finite free charge \(q\), \(\vec{F}=0\). The sign of a charge can affect the direction of force, but here the electric field itself is zero, so the force is zero.

The governing concept is electrostatic equilibrium. A potential difference within a conductor indicates an electric field, since the field is related to the spatial change of potential. Free charges experience electric force and redistribute through the conductor. In the ideal equilibrium state, the interior becomes equipotential and the electric field inside is zero. Therefore A is correct; charges do not disappear or merely remain still, and colour has no physical relevance here.

During rubbing, electrons can transfer between two surfaces, leaving the insulator with a net charge. In an insulator, charge carriers have very low mobility, so the transferred charge cannot move easily through the material and may remain localized. In contrast, free electrons move much more easily in a conductor, so charge is redistributed quickly.

An insulating stand provides a very high-resistance path between the conductor and Earth. Therefore, charge given to the conductor cannot easily flow to Earth, so charge leakage is reduced. In contrast, an insulating stand neither changes the conductor’s mass nor destroys its charge.

Connecting the conductor to Earth through a conducting wire provides a conducting path; this is called earthing. Excess charge flows to Earth, so the conductor is discharged rapidly and becomes neutral. In contrast, an insulating rod or dry glass does not provide an effective conducting path for charge to flow away.

Properly rated, dry, undamaged rubber is an electrical insulator with very high resistance. Therefore, if a person accidentally touches a live conductor, rubber gloves greatly reduce the current that can pass through the body. In contrast, metals contain free electrons and have low resistance, so a metal glove can provide a conducting path for current. Option B is incorrect because rubber is protective due to its high, not low, resistance.

In a neutral conductor, the total positive and negative charges are equal, so its net charge is zero. When a charged object is brought nearby, free electrons move from one region to another due to attraction or repulsion, whereas the positive ion lattice generally remains fixed. Thus, opposite charges can appear on different regions of the conductor while its total charge remains zero. Option B is incorrect because neutrality does not mean the absence of charged particles; it means that positive and negative charges balance overall.

In electrostatic equilibrium, free charges have redistributed on the conductor’s surface. If the electric field inside were non-zero, free charges would experience an electric force and produce a net directed drift. Therefore, the electric field in the interior of the conductor is zero. Charges may still have microscopic random thermal motion, but this does not constitute net directed drift.

The governing concept is charge redistribution in connected conductors. When identical metal spheres touch, free charges can move across their common contact until both reach the same electric potential. If their initial total charge is Q and the arrangement is symmetric, the final charge is typically Q/2 on each sphere, subject to the stated conditions. Thus option A is correct. Charge is conserved, it does not remain confined to the first sphere, and contact does not turn metals into insulators.

In a metal, free electrons redistribute in response to an electric field. At electrostatic equilibrium, this redistribution makes the electric field inside a conductor zero, so the conductor is equipotential. In an insulator, charges are mostly bound to atoms or molecules and cannot redistribute freely throughout the material. Therefore, an electric field and a potential difference can generally remain inside an insulator. Option B is a property of a conductor in electrostatic equilibrium, not of an insulator.

In an insulator, charges are normally bound and cannot move freely through the material as they do in a conductor. When an external electric field is applied, the centres of bound positive and negative charges undergo a very small relative displacement, so the insulator becomes polarized. This is polarization, not a sustained electric current; therefore, option C is incorrect.

Copper has many free electrons, so it has low resistance and allows electric current to flow readily. Rubber has very high resistance, so it forms an insulating outer covering that reduces current leakage and the risk of electric shock. In option B, the conducting copper surface would be exposed to the user, while rubber in the core would not carry current effectively.

The electric-field energy density is \(u=\frac{1}{2}\varepsilon E^2\). In electrostatic equilibrium, \(E=0\) in the interior of a conductor, so \(u=0\). The conductor may have a non-zero electric potential, but energy density depends on the electric field rather than on the potential itself; hence option D is not correct.

In electrostatic equilibrium, free charges redistribute so that the electric field inside the conductor becomes zero. When different parts of the surface have different curvatures, different local surface charge densities may be required to maintain this equilibrium. Generally, charge density is greater near sharp or highly curved regions. In contrast, a symmetric conductor such as a sphere has uniform surface charge density, but this is not true for every shape.

The governing concept is electrostatic equilibrium in conductors. Because free charges can move, mutual repulsion redistributes any excess charge until the electric field inside the conducting material becomes zero. The excess charge therefore resides on the outer surface, although charge may also occur on an inner surface if a cavity contains charge. Thus A is correct; the other options contradict charge conservation or the conducting nature of the material.

The governing idea is that material properties control the mobility of charge. In conductors, many electrons are relatively free to move, so charge can redistribute and reach electrostatic equilibrium. In insulators, charges are more tightly bound and usually remain localized, though polarization can occur. Therefore A correctly connects material nature with charge motion and distribution. Colour, mass alone, and equal conduction do not explain this distinction.

Free charges in a conductor can move. If an electric field existed inside the conductor, it would cause these charges to move; therefore, they redistribute until the field produced by the redistributed charges cancels the field within the conductor. Hence, in electrostatic equilibrium, the net electric field inside a conductor is zero. Option B is incorrect because a conductor may be charged.

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.