Conductors and Insulators

Free charges in a conductor can move. A tangential electric field at the surface exerts a force parallel to the surface on surface charges, causing them to move and redistribute. This redistribution continues until the field produced by the redistributed charges cancels the tangential component. Thus, in electrostatic equilibrium, the electric field at a conductor's surface can only be normal to the surface; a normal field does not drive charges along the surface.

Because Earth is extremely large, it has a very large capacitance. Hence, transfer of charge produces only a very small change in its potential, since
\(\Delta V=\frac{Q}{C}\). Therefore, Earth can receive or supply a large amount of charge while remaining at nearly constant potential. Option B is incorrect because Earth provides a path for charge flow through conducting connections; it is not a perfect insulator.

A metal sphere is a conductor. If it is supported by a conducting path connected to Earth, excess charge can flow to Earth. An insulating rod electrically isolates the sphere from Earth and prevents this loss of charge. Uniform distribution of charge is due to the conducting nature of the sphere, not due to the insulating rod.

A metal is a conductor, so excess charge on it can move easily. A dry insulating handle isolates the rod from the hand and Earth, preventing a path for charge leakage; therefore, the rod can remain charged longer. In contrast, in option B the hand and body can provide a conducting path to Earth, allowing charge to leak away.

When the conductor is connected to the Earth through a conducting wire, charge flows between them until their potentials become equal. Because the Earth has an enormously large size and capacitance, its potential remains practically unchanged; hence the conductor acquires the Earth’s potential. A glass enclosure or an insulating stand keeps the conductor electrically isolated from the Earth, so this equalisation does not occur.

The governing concept is the relation between surface charge density and the electric field near a conductor. A pointed region has a small radius of curvature, so charge tends to accumulate there. Greater surface charge density produces a greater field just outside the conductor; in simplified form, the normal field is proportional to surface charge density. Therefore option A is correct. Option B confuses the zero field inside with the external field, while C and D are not generally true.

A lightning conductor is a metal conductor. When it is earthed, it provides a low-resistance path for lightning current to reach the earth. Thus, the current passes through the conductor and earthing wire rather than through the building. Option B is incorrect because charge may still appear on the conductor; earthing safely carries the resulting current to the earth.

Metals have low electrical resistance because they contain mobile electrons, so the inner metal part carries current. Plastic has very high resistance; its outer covering greatly reduces current flow into a person or another object during accidental contact with the metal conductor, reducing the risk of electric shock. Option B reverses the properties of a conductor and an insulator.

A closed metal body acts as a conducting enclosure. During a lightning strike, current flows mainly along the vehicle's outer metal surface, so the electric field inside is very small. This is the Faraday-cage, or electrostatic-shielding, effect. For safety, a person should avoid touching metal parts of the vehicle. Option B is incorrect because the main protection is due to the conducting metal enclosure, not the rubber tyres.

A negatively charged object repels the free electrons in the conductor toward the farther end. The nearer end is therefore deficient in electrons and acquires an induced positive charge. The conductor still has zero net charge overall because an equal induced negative charge accumulates at the farther end.

A positively charged object attracts the free electrons in the conductor. Hence, electrons accumulate at the nearer end, making that end negative. This is redistribution of charge by electrostatic induction: electrons are neither created nor destroyed, and they do not leave the conductor. The conductor remains net neutral, while its farther end becomes relatively positive. Unlike option B, electrons move toward, not away from, the positive object.

Dry wood generally has very few mobile charge carriers and therefore behaves approximately as an insulator. In wet wood, dissolved salts and other impurities in the moisture can provide ions. These ions move in an electric field and increase the current. Option B is incorrect because wet wood does not acquire metallic free-electron conduction; the increase is mainly due to ionic conduction.

Free charges in a conductor move until the electric field within its material becomes zero. Since \(\vec{E}=-\nabla V\), a zero electric field means that the potential is the same at all points of the conductor. Therefore, option A is correct. Unlike option B, the electric field inside a conductor is zero in electrostatic equilibrium; excess charge generally resides on its surface rather than throughout its volume.

A conductor has many mobile charge carriers. Therefore, excess charge moves quickly and redistributes over the outer surface of the conductor. An insulator has very few mobile charge carriers, so deposited charge generally remains localized near the region where it was placed. Option B incorrectly reverses this difference in charge mobility.

In electrostatic equilibrium, free charge on a conductor arranges itself on its surfaces, and the surface charge density is generally not uniform. It depends on the shape and local curvature of the surface; charge density is higher near sharp regions or regions with a smaller radius of curvature. Although the electric field inside a conductor is zero, this does not imply that the surface charge density is uniform.

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.