Confused by surface charge and voltages

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SUMMARY

A conducting sphere can exhibit a surface charge without having a voltage at its surface due to the influence of an external charge distribution. The electromagnetic field from the external charges causes the free-moving charges within the sphere to redistribute, resulting in a constant electric potential across the surface. This phenomenon occurs because, in the stationary limit, the tangent components of the electric field must vanish to prevent current flow along the surface, as dictated by Ohm's Law, where \(\vec{j}=\sigma \vec{E}\).

PREREQUISITES
  • Understanding of electrostatics and electric fields
  • Familiarity with Ohm's Law and its implications
  • Knowledge of charge distribution and its effects on conductors
  • Concept of electric potential and its relationship to surface charge
NEXT STEPS
  • Study the principles of electrostatics in depth
  • Explore the behavior of electric fields around conductors
  • Learn about charge distribution in conductive materials
  • Investigate the implications of Ohm's Law in static and dynamic scenarios
USEFUL FOR

Physics students, electrical engineers, and anyone interested in understanding the behavior of electric fields and charges in conductive materials.

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How can a conducting sphere have no voltage at the surface, and yet have a surface charge when there's a charge outside of the sphere? Wouldn't the surface charge create voltage at the surface?
 
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A conducting sphere means that it consists of a material, where charges are (quasi-)free to move around. Thus, if you bring a charge distribution outside of the sphere, their electromagnetic field acts on the free-moving charges such that in the stationary limit the sphere becomes a surface of constant electric potential, because then and only then the tangent components of the electric field vanish along the sphere, and this they have to, because in the stationary limit there must be no current along the surface, and there was a current, if the tangent components of the electric field were not vanishing because of Ohm's Law \vec{j}=\sigma \vec{E}.
 

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