Potential of a dipole with actual physical extension?

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SUMMARY

The discussion focuses on the potential of a dipole with physical extension, specifically analyzing a metal sphere with radius R and a defined dipole moment. It establishes that when the surface charge varies as cos(theta), the external field mirrors that of an ideal dipole located at the sphere's center. Additionally, it concludes that the electric field inside the sphere remains constant. The application of Coulomb's law is emphasized for determining the actual field configuration.

PREREQUISITES
  • Understanding of dipole moments in electrostatics
  • Familiarity with Coulomb's law
  • Knowledge of electric field concepts
  • Basic principles of spherical symmetry in physics
NEXT STEPS
  • Explore the mathematical derivation of dipole potential in spherical coordinates
  • Study the implications of varying surface charge distributions on electric fields
  • Investigate the behavior of electric fields inside conductive materials
  • Learn about the applications of dipole fields in real-world scenarios, such as antennas
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetism who are interested in the behavior of electric fields generated by extended charge distributions.

Gavroy
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I think everybody here knows the equation that gives the potential of a point like dipole, but how does the field look like if you have e.g. a metal sphere with radius $R$ and a certain dipol moment, how does this potential look like?
 
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If the surface charge varies like cos theta, the field outside will equal to that of an ideal dipole in the center of the sphere. Inside the sphere, the field is constant. Using Coulombs law it is easy to work out the actual field configuration.
 

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