. A neutral conducting sphere contains a spherical cavity. A point charge +q is located at the |center of the cavity.



A. What is the total surface charge on the interior surface of the conductor?

B. What is the total charge on the exterior surface of the conductor?

A. -q

B. q

Both follow from Gauss' law. Consider a spherical surface inside the metal between the interior and exterior surface (for A.). There can be no E-field flux through that surface, so the total charge inside must be zero.
Outside the sphere (for B.), the net flux is due to the charge at the center, because the surface charges on the inside and exterior of the sphere cancel.

A. To find the total surface charge on the interior surface of the conductor, we need to consider the charge distribution within the sphere. Since the sphere is neutral, the total charge within the sphere must be zero.

The charge distribution inside the conductor will redistribute itself in order to cancel out the charge of the point charge at the center of the cavity. This implies that the negative charge on the inner surface of the conductor will attract the positive charge of the point charge and they will redistribute such that the total charge within the sphere is zero. As a result, the total surface charge on the interior surface of the conductor will be -q.

B. Since the sphere is neutral, the total charge on the exterior surface of the conductor will also be zero. This is because the net charge within an isolated conductor must always be zero, meaning any charge on the exterior surface would have an equal and opposite charge distributed elsewhere within the conductor. Therefore, the total charge on the exterior surface of the conductor is zero.

To answer these questions, we need to understand how charges distribute on a neutral conductor and its cavity.

When a conducting sphere is neutral, the charges distribute themselves in a manner such that the electric field inside the conductor is zero. Therefore, charges on the interior surface get rearranged due to the presence of the charge in the cavity.

A. To determine the total surface charge on the interior surface of the conductor, we need to consider the distribution of charges. Since the charge inside the cavity is +q, the induced charges on the interior surface will be -q to neutralize the electric field produced by the charge within the cavity. So the total surface charge on the interior of the conductor is -q.

B. To determine the total charge on the exterior surface of the conductor, we need to consider the fact that conductors are electrically neutral on the outside. Due to the presence of the charge +q inside the cavity, an equal amount of negative charge (-q) will distribute itself on the exterior surface of the conductor in order to maintain overall neutrality. Therefore, the total charge on the exterior surface of the conductor is also -q.

In summary,
A. Total surface charge on the interior: -q
B. Total charge on the exterior: -q