Potentials of Hollow and Solid Spheres

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SUMMARY

The discussion focuses on the electric potential of hollow and solid spherical conductors, specifically a hollow spherical conductor with a radius of 3.00 cm and a charge of 6.00 nC. The electric potential at the center of both hollow and solid conductors is the same, as the potential inside a conductor is uniform and equal to the potential on its surface. The formula V(r) = kQ/r, where k = 1/4πE₀, is used to derive these potentials, confirming that the distribution of charge does not affect the potential within the conductor.

PREREQUISITES
  • Understanding of electric potential and electric fields
  • Familiarity with the formula V(r) = kQ/r
  • Knowledge of conductors and charge distribution
  • Basic principles of electrostatics
NEXT STEPS
  • Explore the concept of electric fields within conductors
  • Learn about Gauss's Law and its application to spherical conductors
  • Investigate the differences between conductors and insulators in electrostatics
  • Study the implications of charge distribution on electric potential in various geometries
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Students of physics, electrical engineers, and anyone interested in understanding electrostatics and the behavior of electric fields in conductors.

cwatki14
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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\piE\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?
 
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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.
 

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