Is the Potential Constant Inside a Spherical Conductor/Insulator?

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SUMMARY

The electric potential inside a spherical conductor or insulator is constant due to the absence of an electric field (E-field) within the conductor. This phenomenon occurs because the E-field inside the conductor is zero, leading to a uniform potential throughout its interior. To calculate the potential, one must select a reference point where the potential is defined as zero, commonly at infinity, unless the charge distribution alters this condition, necessitating an alternative reference point.

PREREQUISITES
  • Understanding of electrostatics and electric fields
  • Familiarity with the concept of electric potential
  • Knowledge of boundary conditions in physics
  • Basic calculus for integrating electric fields to find potential
NEXT STEPS
  • Study Gauss's Law and its application to spherical conductors
  • Learn about electric field calculations in different charge distributions
  • Explore boundary value problems in electrostatics
  • Investigate the concept of reference points in potential energy calculations
USEFUL FOR

Physics students, electrical engineers, and anyone interested in understanding electrostatics and electric potential in conductors and insulators.

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why is the potential constant inside a spherical conductor/insulator? Are there boundary conditions that needs to be satisfied in order to make the potential zero?

this is just a general question since most of the physics problems that I do needs the potential to be constant inside the sphere.
 
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the potential inside a spherical conductor is constant (at the value that it reaches at the surface of the sphere) because the E-field inside the conductor is zero.

In order to calculate the potential you need to choose a spot where the potential is zero as a reference point for the integral. Normally, choosing infinity works just fine. However, if you have a charge that goes to infinity (such as an infinitely long charged rod) the potential does not go to zero at infinity and the best choice is typically zero or an arbitrary point a.
 

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