Electrostatics and Charge Distribution

Both solid and hollow conducting spheres with the same radius will hold the same maximum charge due to their identical electric field properties. When charged, the distribution of charge occurs on the outer surface of both types of spheres, leading to the same surface charge density. The ability to hold charge is determined by the surface area and the nature of the conductor, not its volume or whether it is hollow or solid. Hence, both spheres can accommodate an equal amount of charge without affecting their electric field.

When object B is rubbed against object C, the triboelectric effect comes into play, where electrons are transferred between the two substances. If B has already become positively charged after rubbing with A, it means that B has lost electrons. When B rubs against C, B will attract electrons from C, making B even more positively charged. Consequently, C will lose electrons and become negatively charged. This transfer of charge explains why B becomes positively charged and C becomes negatively charged.

When two conductive spheres are connected, charge redistributes between them until they reach the same potential. The potential \( V \) of a sphere is given by \( V = \frac{kQ}{r} \), where \( k \) is a constant, \( Q \) is the charge, and \( r \) is the radius. For the two spheres, the potentials must equalize. Setting the potentials equal and solving for the final charge on the larger sphere, we find that it ends up with 3 × 10⁻² C, balancing the total charge while considering their different radii.

When two conductive spheres are brought into contact, they share their total charge in proportion to their capacitance, which depends on their radii. The capacitance of a sphere is directly proportional to its radius. Here, the smaller sphere (radius R) has a charge of 15C, and the larger sphere (radius 4R) has a charge of -5C. The total charge is 10C. The capacitance ratio is 1:4, so the smaller sphere will have 2C, and the larger sphere will have 8C after contact, reflecting the distribution based on their sizes.

When the spheres come into contact, charge redistributes to equalize the potential across them. First, when X (Q) and Y (-2Q) touch, they share a total charge of -Q, resulting in each having -Q/2. Next, Y (-Q/2) and Z (3Q) touch, sharing a total of 5Q/2, giving each a final charge of 5Q/4. Therefore, after both contacts, the final charges are X: -Q/2, Y: 5Q/4, and Z: 5Q/4.

When a point charge is placed near an uncharged conducting sphere, it induces a separation of charges within the sphere. The side of the sphere closest to the point charge acquires a negative charge, while the opposite side becomes positively charged. However, since the sphere remains neutral overall, the total induced charge on the sphere sums to zero. Thus, while there are induced charges, the net charge on the sphere itself does not change and remains zero.

When substance A rubs against substance B, the process of friction causes the transfer of electrons. In this case, A becomes positively charged, indicating that it has lost electrons. Since electrons carry a negative charge, losing them results in a net positive charge for A. Conversely, substance B, having gained these electrons, becomes negatively charged. Thus, the interaction leads to A losing electrons to B, which is why A is positively charged after the rubbing process.

When a point charge is brought near a conducting sphere, it induces a separation of charges within the sphere. The side of the sphere closest to the point charge accumulates opposite charge due to attraction, while the far side develops a corresponding positive charge. This results in a non-uniform charge distribution, with the concentration of opposite charge on the near side and an overall neutral state maintained. Thus, the charge distribution on the sphere is non-uniform, with opposite charge facing the inducing point charge.