Potentials of Hollow and Solid Spheres

[cwatki14]

A hollow spherical conductor of radius 3.00 cm has 6.00 nC of charge distributed uniformly over its surface.
(a)What is the electric potential at the center of the sphere(in volts)?
(b) If the conductor is solid rather than hollow, what is the potential at the center of the sphere?

I know V(r)=kQ/r
where k= 1/4$$\pi$$$$E$$$$\circ$$

I also know that conductors have charges only present on the surface.
How does a solid conductor differ from a hollow one, if they do? If they don't have potential differences, why is this?

 

[kuruman]

As far as the potential is concerned, a hollow conductor is no different from a solid one. The potential inside a conductor is everywhere the same which means that the potential inside is the same as the potential on the surface. This is so because conductors have gazillions of charges (electrons) that are free to move much like the air molecules in a room. If there is a potential difference in the conductor, there would be an electric field which will exert a force on these electrons which will move and keep on moving until they have no more reason to move, i.e. until the electric field becomes zero. When the electric field is zero, the potential is the same everywhere.

 

[tomcue]

(a) The electric potential at the center of the hollow spherical conductor can be calculated using the equation V(r) = kQ/r, where k is the Coulomb's constant, Q is the charge on the surface of the sphere, and r is the radius of the sphere. Therefore, the potential at the center of the sphere would be V(0) = (9.0 x 10^9 Nm^2/C^2)(6.00 x 10^-9 C)/(0.030 m) = 1.80 x 10^6 V.

(b) If the conductor is solid rather than hollow, the potential at the center of the sphere would be the same. This is because the charge is still uniformly distributed over the surface of the sphere, and the distance from the center to any point on the surface is still the same. Therefore, the equation V(r) = kQ/r would still hold true, and the potential at the center would be the same as in the hollow sphere case.

The main difference between a solid and hollow conductor is the distribution of charge. In a solid conductor, the charge is distributed throughout the entire volume, whereas in a hollow conductor, the charge is only present on the surface. However, when calculating the electric potential at a point inside the conductor, the charge distribution outside that point does not affect the potential. This is because the electric field inside a conductor is always zero, so the charge distribution outside does not contribute to the potential at that point. Therefore, the potential at the center of both a solid and hollow conductor is the same.