Show the equipotential surface is a spherical surface

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SUMMARY

The discussion centers on demonstrating that the equipotential surface V=0, associated with a system of two charges (a point charge q located at (a,0,0) and a point charge -q/2 at (-a,0,0)), is a spherical surface. The participants conclude that the center of this sphere is at the origin (0,0,0) and the radius can be determined based on the distances from the charges. The analysis of equipotential surfaces is essential for understanding electric fields and potentials in electrostatics.

PREREQUISITES
  • Understanding of electrostatics and electric fields
  • Familiarity with the concept of equipotential surfaces
  • Knowledge of point charges and their potential equations
  • Basic skills in three-dimensional coordinate geometry
NEXT STEPS
  • Study the mathematical derivation of electric potential from point charges
  • Learn about the properties of equipotential surfaces in electrostatics
  • Explore the implications of spherical symmetry in electric fields
  • Investigate the concept of superposition in electric potentials
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching electrostatics, and anyone interested in the mathematical modeling of electric fields and potentials.

blueyellow

Homework Statement



consider now a system of two charges: a point charge q>0 located at the position (x,y,z)=(a,0,0) and a point charge -q/2 located at (-a,0,0).Show that the equipotential surface V=0, i.e. with the same potential than at infinity, is a spherical surface. Determine the centre and the radius of the sphere.

The Attempt at a Solution


tried looking up equipotential surfaces. couldn't find much
 
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hi blueyellow! :smile:
blueyellow said:
tried looking up equipotential surfaces. couldn't find much

an equipotential surface is pretty much what it says on the tin!

start by finding the two points on the x-axis with potential zero :wink:
 

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