Question

a positive charge is kept (fixed) off - center inside a fixed spherical conducting shell that is electrically neutral, and the charges in the shell are allowed to reach electrostatic equilibrium. the large positive charge inside the shell causes equal in magnitude charges distributed on the inner and outer surfaces of the spherical shell. which of the following figures best represents the charge distribution on the inner and outer walls of the shell? (figure 1) view available hint(s) options: 1, 2, 3, 4, 5 with radio buttons; submit; provide feedback; next

Explanation:

For a neutral conducting shell with a fixed off - center positive charge inside:

1. Inner Surface: The inner surface will have a non - uniform negative charge distribution. This is because the electric field inside the conducting material (of the shell) must be zero. The off - center positive charge will induce a negative charge on the inner surface, and the distribution of this negative charge will be such that it cancels the electric field from the central positive charge within the conductor. So, the negative charges on the inner surface will be more concentrated closer to the off - center positive charge.
2. Outer Surface: The outer surface will have a uniform positive charge distribution. The reason for this is that the charge on the outer surface is not affected by the position of the inner charge (due to the shielding effect of the conducting material). The total charge on the outer surface is equal in magnitude to the charge on the inner surface (to keep the shell neutral overall, and since the shell was initially neutral and the inner charge induced a negative charge on the inner surface, the outer surface gets a positive charge of equal magnitude). Also, for a conducting shell, the charge on the outer surface distributes uniformly because there is no net electric field inside the conductor to influence its distribution (the electric field due to the inner charge and the induced inner - surface charge cancels out within the conductor, so the outer - surface charge experiences no net force and distributes uniformly).

Looking at the figures, Figure 2 should represent this situation. On the inner surface, the negative charges are non - uniformly distributed (more near the off - center positive charge), and on the outer surface, the positive charges are uniformly distributed.

Answer:

2 (assuming the figure labeled 2 has non - uniform negative charge on the inner surface and uniform positive charge on the outer surface)