Final answer:
A spherical conductor of radius a carries a charge that is uniformly distributed over its surface. The uniform distribution of charge is due to the repulsive forces between like charges, resulting in an even spread of charge on the spherical surface.
Step-by-step explanation:
A spherical conductor of radius a carries a total charge that is uniformly distributed over its surface due to the property of electric charge redistribution on conductors. When a charge is placed on a spherical conductor, or when the conductor is brought into contact with a charged object, it will distribute evenly across the surface, resulting in a uniform surface charge density. This is a consequence of the fact that like charges repel one another, and the charges strive to be as far away from each other as possible, which, on a spherical surface, results in a uniform distribution.
For example, if we have a metallic sphere of radius 2.0 cm and it is initially charged with a +5.0-μC charge, this charge will spread uniformly across the surface of the sphere. If this sphere is then brought into contact with another conductor or has additional charge placed on or near it, the total charge of the system will redistribute across the surfaces according to electrostatic principles. Similarly, the presence of a cavity or other changes to the internal structure of the conductor does not affect the external surface charge distribution, which will always remain uniform due to the conductor's ability to freely move charges.