Conductors and Insulators

Correct answer: D. The net charge remains unchanged

Explanation: In polarisation, the centres of bound positive and negative charges in an insulator are displaced slightly. This separates charge and may produce bound charges on its surfaces, but charge is neither created nor destroyed. Therefore, if no charge is transferred from outside, the insulator’s net charge remains unchanged; this is different from the net charge becoming positive.

Correct answer: A. Negative induced charge

Explanation: The negatively charged rod repels the conductor’s free electrons. The electrons redistribute toward the end farther from the rod, so that end acquires a negative induced charge. The nearer end becomes positive because it has a deficiency of electrons. The conductor’s total charge remains zero; only the charge distribution changes.

Correct answer: A. Induced positive charge

Explanation: The positively charged rod attracts the conductor’s free electrons toward the nearer end. The farther end is therefore deficient in electrons and develops an induced positive charge. This is charge separation, so the isolated conductor still has zero net charge overall. Induced negative charge appears at the end nearer the rod, not at the far end.

Correct answer: A. Zero

Explanation: In electrostatic equilibrium, the electric field inside a conductor is \,\(\vec{E}=0\). Hence \(\Delta V=-\int \vec{E}\cdot d\vec{l}=0\). Therefore, all points inside the conductor are at the same potential. The conductor may have a non-zero potential due to its charge, but the potential difference between any two internal points is zero.

Correct answer: A. Electric discharge

Explanation: For a charged conductor, excess charge accumulates more densely at regions of small radius of curvature, such as a sharp tip. The electric field just outside the tip therefore becomes very strong. If it exceeds the breakdown strength of the surrounding air, ionisation and electric discharge can occur. Hence option A is correct. The effect does not increase mass, cancel magnetism or destroy charge; it concerns field strength and discharge.

Correct answer: B. Earth's potential, conventionally taken as zero

Explanation: Earth acts as an extremely large conductor and charge reservoir. When the sphere is grounded, charge flows until the potential difference between the sphere and Earth becomes zero. Hence, in electrostatic equilibrium the sphere is at Earth's potential, conventionally taken as zero. Option A is incorrect because the initial potential does not remain unchanged.

Correct answer: A. Zero

Explanation: Electrostatic induction separates the existing positive and negative charges inside a neutral conductor; it does not create charge. If the conductor is isolated and there is no earthing, no charge can enter or leave, so conservation of charge requires its net charge to remain zero. Thus option A is correct. The conductor may have opposite charges on different regions, but their algebraic sum remains zero; it is not automatically positive, negative or infinite.

Correct answer: A. Charge flows to the Earth through the hand and body.

Explanation: A metal is a conductor, so its free electrons and any excess charge can move easily. When the rod is held, the hand and body provide a path for charge to flow to the Earth, especially when the person is in contact with the ground. Thus, the charge is not destroyed; it leaks from the rod to the Earth, leaving the rod nearly neutral. Option C is incorrect because friction does not destroy charge.

Correct answer: A. The insulating handle greatly reduces the path for charge to leak from the rod through the hand to Earth.

Explanation: Because a metal rod has free electrons, charge can move through it. If the rod is held directly, a conducting path through the hand and body to Earth can allow charge to leak away. An insulating handle greatly reduces this conducting path, so the charge can remain for longer. The handle neither creates charge nor changes the metal into an insulator; some leakage may still occur through air or surface moisture.

Correct answer: A. Because the effect of an external electrostatic field becomes zero inside the enclosure.

Explanation: In electrostatic equilibrium, free charges on a closed conducting enclosure redistribute over its surfaces. This redistribution cancels the electric field produced by external charges within the enclosure. Therefore, if no charge is present in the cavity, the effect of an external electrostatic field inside is zero and the device is protected. This is not due to an increase of current in the device; it is due to the zero electric field inside.

Correct answer: A. Conductors have mobile free charge carriers, whereas charges in insulators are mainly bound.

Explanation: In a conductor, free electrons or other free charge carriers can move through the material. They redistribute until the electric field inside the conductor becomes zero in electrostatic equilibrium; hence, excess charge resides on its surface. In an insulator, charge carriers are bound and cannot move freely through the material, so deposited charge generally remains localized. Option C is incorrect because Coulomb repulsion between charges does not become weaker merely because the material is an insulator.

Correct answer: A. Opposite charge effect can form

Explanation: The governing concept is electrostatic polarisation. In an insulator, charges are bound to atoms or molecules, so they cannot flow through the material, but they can shift slightly in opposite directions. The nearer surface therefore develops an induced effect opposite to the rod’s charge, and the stronger nearby attraction can exceed the distant repulsion. Thus A is correct; the other choices contradict charge conservation or basic gravity.

Correct answer: A. Because free charges in the metal redistribute and produce a field opposing the external field.

Explanation: A metal is a conductor, so its free electrons redistribute in response to an external electrostatic field. This redistribution produces induced charges that create an electric field opposing the external field. Hence, the resultant electric field in the region inside the mesh is reduced; this is electrostatic shielding. Option D is not correct because some field can enter through mesh openings, and the amount of shielding depends on the mesh openings and geometry.

Correct answer: A. It increases in the same proportion.

Explanation: For a conductor in electrostatic equilibrium in vacuum, the magnitude of the electric field just outside the surface is \(E=\sigma/\varepsilon_0\), where \(\sigma\) is the local surface charge density. Therefore, when \(\sigma\) increases, \(E\) increases in the same proportion. In contrast, the electric field inside the conductor is zero; the field just outside the surface is not zero.

Correct answer: A. Because it retains in the conductor the net charge acquired through Earth while the inducing body is nearby.

Explanation: When the charged inducing body is brought near the conductor, charges separate within the conductor. On earthing, electrons may enter the conductor from Earth or leave it for Earth. Removing the earth connection while the inducing body is still nearby traps this net charge on the conductor. If the inducing body were removed first while the earth connection remained, charge could flow to or from Earth and neutralize the conductor. Therefore, A is correct; unlike B, the purpose of the correct sequence is not to keep the conductor neutral, but to leave it with a net induced charge.

Correct answer: A. Its net charge remains zero; only charge redistribution occurs.

Explanation: The electric field of the charged rod redistributes the conductor’s free charges, producing polarization by induction. However, because the conductor is isolated and neither touches the rod nor is grounded, no charge can enter or leave it. Therefore, its net charge remains zero. If it were grounded, charge could flow to or from Earth and the conductor could acquire a net charge.

Correct answer: A. Non-zero surface charge density

Explanation: In electrostatic equilibrium, the electric field inside a conductor is zero, and the tangential component of the field at its surface is also zero. The normal component just outside the surface is related to the surface charge density $\sigma$ by $E_{\perp}=\sigma/\varepsilon_0$ (in vacuum). Therefore, a non-zero $E_{\perp}$ indicates a non-zero surface charge density. It does not necessarily imply that the conductor has a non-zero net charge, because a neutral conductor can have induced surface charges.

Correct answer: A. Yes, if the algebraic sum of the positive and negative induced charges is zero.

Explanation: Electrostatic induction can redistribute the free charges in an isolated conductor. Positive induced charge may appear on one part of its surface and negative induced charge on another, but the conductor remains neutral when their algebraic sum is zero. Local charge separation is different from the conductor's total (net) charge; connecting it to the Earth is not required for this situation.

Correct answer: A. Zero

Explanation: In electrostatic equilibrium, the electric field within the material of a conductor is zero, i.e., \(E=0\). The electric-field energy density is \(u=\frac{1}{2}\varepsilon_0E^2\). Therefore, when \(E=0\), \(u=0\). Surface charge can produce an electric field and field energy outside the conductor, but the energy density within the conducting material remains zero.

Correct answer: A. The excess charge will remain mainly localized near that region

Explanation: In an insulator, electrons or other charge carriers are bound to atoms or molecules and cannot move freely through the material over large distances. Hence, excess charge placed in a small region generally remains localized near that region. In contrast, free electrons in a conductor can redistribute charge rapidly, so option B is closer to the behavior of a conductor.

Correct answer: A. Dissolved salts and impurities in moisture provide ions that act as charge carriers.

Explanation: Dry wood is generally an insulator because it has very few mobile charge carriers. In wet wood, dissolved salts and other impurities in the moisture provide ions. These ions can move and carry electric current, so the electrical conductivity of the wood can increase. Unlike metals, wood does not conduct mainly through free electrons.

Correct answer: A. Free charges will start moving

Explanation: Different potentials at points inside a conductor imply a non-zero electric field, since
\(\vec{E}=-\nabla V\). This field exerts a force on free charges, so they start moving. Charges redistribute until electrostatic equilibrium is reached; at equilibrium, the electric field inside the conductor is zero and the conductor is equipotential. Option C describes the final equilibrium condition, not the immediate consequence.

Correct answer: A. Induced charges rearrange on the conductor’s surface so that the resultant electric field in the cavity is zero

Explanation: In electrostatic equilibrium, free charges in a conductor rearrange until the electric field within the conducting material becomes zero. An external charge induces a surface-charge distribution on the conductor. The boundary of the empty cavity is an equipotential surface, so the potential throughout the cavity is constant and the electric field is zero. Option D is incorrect because a conductor need not be at zero potential; its potential is merely the same throughout the conductor.

Correct answer: A. At the sharpest part, with the smallest radius of curvature

Explanation: In electrostatic equilibrium, charge is not distributed uniformly over an irregular conductor. A region with a smaller radius of curvature, that is, a sharper region, has a greater surface charge density. Therefore, option A is correct. In contrast, a flatter region with a larger radius of curvature generally has lower charge density.

Correct answer: A. The potential difference between any two points of the conductor is zero.

Explanation: In electrostatic equilibrium, free charges in a conductor redistribute until the electric field inside it becomes zero. Hence, all points of the conductor are at the same potential, so the potential difference between any two points is zero. Being equipotential does not imply zero net charge; a conductor may have a nonzero net charge and still be equipotential.