Conductors and Insulators

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.