Conductors and Insulators

Correct answer: A. To connect the metal casing to Earth, providing a safe path for excess or leakage charge and keeping the casing near earth potential

Explanation: Earthing connects the metal casing to Earth. Earth is a very large conductor that can accept or supply charge with negligible change in its potential. Thus, excess or leakage charge can flow safely to Earth and the casing remains near earth potential, reducing the risk of electric shock. Option B is incorrect because earthing does not make a conductor an insulator; it provides a safe conducting path for charge.

Correct answer: A. \(q_1:q_2=R_1:R_2\)

Explanation: Conductors connected by a wire attain the same potential at electrostatic equilibrium. For an isolated conducting sphere, \(C=4\pi\varepsilon_0R\) and \(q=CV\). Since both spheres have the same potential \(V\), \(q_1:q_2=C_1:C_2=R_1:R_2\). Thus, unequal spheres do not generally receive equal charges; the ratio \(1:1\) applies only when their radii are equal.

Correct answer: A. After contact, the spheres attain the same potential and have equal capacitances.

Explanation: Contact allows charge to flow from one sphere to the other. At electrostatic equilibrium, the connected conductors are at the same potential. Identical spheres have equal capacitance, so from \(Q=CV\), equal potential gives equal charge on them. Total charge is conserved; it is redistributed rather than destroyed. The initial charges need not be equal, because charge redistributes after contact.

Correct answer: A. When it is polarised by an external charge

Explanation: An insulator normally does not permit sustained conduction current because its charge carriers are bound. However, an external charged body can slightly displace positive and negative charges within its molecules, producing polarisation. The closer induced opposite charge experiences a stronger force, so attraction occurs without charge flowing through the insulator. Therefore A is correct; B changes the material, while C and D are physically impossible descriptions.

Correct answer: A. They experience zero net electric force, so there is no net drift caused by the electric field.

Explanation: In electrostatic equilibrium, the electric field inside the conducting material is zero. Therefore, free charges experience zero net electric force, so there is no net drift or current caused by an electric field. Option B is incorrect because random microscopic thermal motion may still occur; only the net directed drift is zero.

Correct answer: A. Because it has high electrical resistance and limits leakage current to a person's body.

Explanation: An insulator has very few mobile free charge carriers, so it has high electrical resistance. A plastic covering confines the current to the metal wire and reduces the chance of leakage current reaching a person's body, thereby helping prevent electric shock. In contrast, a low-resistance conductor allows current to flow easily.

Correct answer: A. Charges rearrange on the surface of the cage

Explanation: This is the principle of electrostatic shielding. In a metal, free charges move under an applied electric field and redistribute themselves over the outer surface. Their induced field opposes the applied field in the enclosed region, making the net internal field very small or zero under ideal electrostatic conditions. Thus A is correct. The cage does not destroy charge, block gravity, or lack charge carriers, as the other options suggest.

Correct answer: A. Because repulsion will continue rearranging charges inside

Explanation: Electrostatic equilibrium requires that free charges have no net force and therefore no continued drift. If excess charge is located within the bulk of a conductor, mutual repulsion and the resulting electric field drive the mobile charges toward the outer surface. Redistribution continues until the internal electric field is zero and excess charge resides on the surface. Therefore A is correct; the other choices do not describe the equilibrium condition.

Correct answer: A. If the electric field had a tangential component, free charges would keep moving along the surface until that component became zero.

Explanation: In electrostatic equilibrium, the free charges in a conductor are at rest. If there were a tangential component of the electric field along the surface, it would exert a force on surface charges and make them move. Charges redistribute until the tangential component becomes zero. Hence, the electric field just outside the surface has only a normal component. Option B is incorrect because the normal component at the surface of a charged conductor is generally not zero.

Correct answer: A. When the conductor is connected to Earth by a metal wire

Explanation: A metal wire provides a low-resistance conducting path between the conductor and Earth. Charge then flows between Earth and the conductor until the conductor reaches approximately Earth’s potential. An insulating stand or a glass layer does not provide such a conducting path, so rapid earthing does not occur.

Correct answer: A. Because an insulator has insufficient free charge carriers for charges to move throughout the material.

Explanation: Rubbing can transfer electrons and create excess charge on a region of an insulator's surface. However, electrons in an insulator are generally bound to atoms or molecules, so there are not enough mobile charge carriers to carry the charge through the material. The charge therefore usually remains localized near the rubbed region. In contrast, free electrons in a conductor can redistribute the charge. Option C describes the behavior of a conductor, not an insulator.

Correct answer: A. A negatively charged metal sphere touches a neutral, isolated metal sphere. After separation, the second sphere acquires negative charge.

Explanation: In charging by contact, a charged conductor makes direct contact with a neutral conductor. In option A, electrons transfer from the negatively charged sphere to the neutral sphere, so the second sphere is negatively charged after they are separated. In option B, there is no contact and only temporary charge separation due to induction occurs; option C describes charging by induction with earthing, whereas option D describes charging by friction.

Correct answer: A. Bringing a charged object near a neutral conductor without touching it, connecting the conductor to earth while the object remains nearby, disconnecting the earth connection first, and then removing the charged object

Explanation: In charging by induction, the charged object does not touch the conductor; it causes separation of charges in the conductor. When the conductor is earthed while the charged object is nearby, electrons flow between the earth and the conductor. Disconnecting the earth connection first leaves the conductor with a net charge; removing the charged object afterwards does not remove this charge. In option D, there is only temporary charge separation, so the conductor does not retain a permanent net charge.

Correct answer: A. Charge separation by induction

Explanation: The governing concept is electrostatic induction. A neutral conductor has equal total positive and negative charge, so its net charge is zero, but an external charged body can attract mobile electrons toward one side and leave the opposite side relatively positive. This spatial separation creates local effects without changing the total charge. Hence A is correct; charge is not destroyed, mass need not change, and the conductor is not an insulator.

Correct answer: A. Rubber has very high resistivity and very few freely mobile charge carriers, so very little current flows through the body.

Explanation: Rubber is an insulator with very high resistivity. It has very few freely mobile charge carriers, so it opposes the flow of current between the electrical source and a person's hand. Consequently, the current through the body is reduced, lowering the risk of electric shock. Option B is incorrect because rubber does not absorb current; it primarily resists the flow of current.

Correct answer: A. Copper has low resistance, whereas plastic has high resistance; therefore, plastic prevents current leakage and electric shock.

Explanation: Copper has many free electrons and low resistance, so it allows electric current to flow easily. Plastic has very high resistance, so it prevents current leakage from the conductor and reduces the risk of electric shock on touching the wire. Option D is incorrect because the main role of plastic covering is electrical insulation and safety, not merely mechanical strength.

Correct answer: A. The electric field inside the conducting material is zero, and excess charge resides on its surface.

Explanation: In electrostatic equilibrium, free charges in a conductor rearrange until the electric field inside the conducting material becomes zero. If an internal electric field were non-zero, it would exert a force on free charges and cause further motion. Therefore, the excess charge on an isolated solid conductor resides on its surface. Option B is incorrect because excess charge is not uniformly distributed throughout the conductor’s volume.

Correct answer: A. Charge can remain localized, and bound charges can become polarized.

Explanation: In an insulator, charge carriers cannot move freely throughout the material, so deposited excess charge may remain localized. An external electric field can cause a small relative displacement of bound positive and negative charges; this is polarization. Option C describes electrostatic equilibrium in a conductor, whereas the electric field inside an insulator need not be zero.

Correct answer: A. Availability of free, mobile charge carriers determined by the material's electronic structure

Explanation: In a conductor, some charge carriers, usually electrons, are relatively free from atoms and can move in an electric field. In an insulator, electrons are tightly bound, so there are very few mobile charge carriers. This difference arises from the material's internal electronic structure, not merely from the number of atoms or the object's shape.

Correct answer: A. Motion, distribution, and shielding of charge depend on the nature of material

Explanation: The broad governing idea is that material structure controls charge behaviour. Conductors have many mobile charge carriers, so charge moves and redistributes readily and can produce shielding. Insulators hold charges more tightly, so charge remains localized and polarisation occurs mainly through small displacements. Thus A correctly combines motion, distribution, and shielding; B, C, and D conflict with the defining electrical properties of materials.

Correct answer: A. Zero electric field inside

Explanation: The governing concept is electrostatic equilibrium in a conductor. If two points inside the conductor had different potentials, a potential gradient and hence an electric field would exist between them. Free charges would then move until this field vanished. Therefore the electric field inside becomes zero and the entire conductor, including its surface, has one potential. Metallic colour, weight, and temperature do not establish the equipotential condition.

Correct answer: A. Because both move toward equal potential on contact

Explanation: When two metal spheres touch, they form one conducting system, so mobile charges can move between them. The transfer continues until both spheres reach the same electric potential. Because the spheres are identical, equal potential also means equal capacitance and therefore equal final charge. If the initial total charge is Q, each sphere finally carries Q/2, provided there is no charge leakage to the surroundings. Charge is conserved; it is not destroyed.

Correct answer: A. They become equipotential but their capacitances can be different

Explanation: Conductors in contact exchange charge until their potentials become equal, not until their charges become equal. For an isolated conductor, Q = CV. Unequal-sized conductors generally have different capacitances, so the same final potential gives different charges: Q1 = C1V and Q2 = C2V. Equal sharing occurs only in special cases such as identical spheres. Charge is conserved and can enter either conductor; size does not block electron motion.

Correct answer: A. Charge density can be high at the sharp tip

Explanation: At electrostatic equilibrium, the surface of a conductor is equipotential, but the surface charge density need not be uniform. Charge crowds more strongly in regions of small radius of curvature, such as a sharp tip. Just outside the conductor, the normal field is related to surface charge density by E = σ/ε0; hence a larger σ produces a stronger local field. A tip is not an insulator, and charge is not destroyed there.

Correct answer: B. The field can become stronger

Explanation: For a conductor in electrostatic equilibrium, the electric field immediately outside the surface is normal to the surface and has magnitude Eout = σ/ε0, where σ is the local surface charge density. Thus, if σ increases at a particular region, the nearby external field increases in magnitude there, with its direction set by the sign of the surface charge. The field is not confined inside the conductor, where it is zero in equilibrium, and it does not convert into mass.