The work done (W) to bring a charge q to a point with an electric potential V is given by W = q * V. Substituting the values, we get W = (4 * 10^-3C) * (2 * 10^2V) = 0.8J. The work done is positive in this case.

In order for charge to flow from the smaller sphere to the larger sphere, the spheres should be placed concentrically, with the smaller sphere positioned inside the larger sphere. When connected with a wire, the charge will redistribute itself on the outer surfaces of both spheres, with some charge flowing from the smaller sphere to the larger sphere.

The electric potential at x = 0 in the infinite series of charges can be calculated as V = 3q/(16πε₀). It takes into account the sum of the potentials of each individual charge, resulting in the given expression.

The term permittivity, often referred to as the dielectric constant, is a fundamental property of a material that determines its ability to store electrical energy in the presence of an electric field. It measures the degree to which the material can be polarized when subjected to an electric field. In other words, permittivity quantifies the electric field response of a material and its capacity to store electrostatic energy.

Insulators primarily serve the function of providing electrical insulation. Insulating materials, also known as insulators, are designed to prevent the flow of electric current through them. Unlike conductors, which readily allow the movement of electrons, insulators have tightly bound electrons that are not easily free to move. This characteristic makes insulators valuable for creating barriers that prevent current leakage and electric shock hazards. Insulators are widely used in electrical and electronic systems to separate conductive elements and ensure the safe and efficient functioning of devices and circuits. By providing electrical insulation, insulators minimize the risk of short circuits, electrical interference, and other undesirable phenomena associated with the uncontrolled flow of electric current.

The susceptibility of free space or air is zero (0). In free space, the relative permittivity (εr) is equal to 1, and the susceptibility (χe) is given by χe = εr - 1 = 1 - 1 = 0. This means that free space does not exhibit any polarization or ability to become polarized under the influence of an electric field.

The susceptibility (χe) can be calculated by dividing the bound charge density by the free charge density. In this case, the ratio is 12/6 = 2. Therefore, the susceptibility is 2. Susceptibility measures the extent to which a material can become polarized when exposed to an electric field.

In a charged conductor, the charges distribute themselves uniformly on its surface. This distribution of charges creates an electric field inside the conductor. However, within a conductor, the electric field is zero, and therefore, the potential is constant throughout its surface, making it an equipotential surface. The electric field lines are perpendicular to the surface of the conductor.

The susceptibility (χe) of a material is defined as χe = εr - 1, where εr represents the dielectric constant. For a material with a dielectric constant of 2.26, the susceptibility is 2.26 - 1 = 1.26. Susceptibility quantifies the degree of polarization of a material in response to an electric field and provides insight into its electrical behavior.

The property that distinguishes conductors, insulators, and semiconductors is the energy band gap. The energy band gap is a characteristic of the electronic structure of materials and represents the energy difference between the valence band (the highest energy band occupied by electrons at absolute zero temperature) and the conduction