Electric potential of a conducting sphere

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SUMMARY

The electric potential of a charged conducting sphere with a radius of 5.5 cm and an electric field of 1667 V/m just outside its surface can be calculated using the relationship between electric field and potential. The potential at infinity is defined as zero, and the electric potential (V) can be determined by integrating the electric field (E) using the formula V = - ∫ E · dl. Applying Gauss's law is essential for calculating the electric field outside the sphere, which is directly related to the charge on the sphere.

PREREQUISITES
  • Understanding of Gauss's law
  • Knowledge of electric fields and potentials
  • Familiarity with calculus, specifically integration
  • Concept of electric potential at infinity
NEXT STEPS
  • Study the application of Gauss's law in electrostatics
  • Learn how to calculate electric potential from electric field using integration
  • Explore the concept of electric potential energy in charged systems
  • Investigate the behavior of electric fields and potentials in spherical symmetry
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone seeking to understand the principles of electric fields and potentials in conductive materials.

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Homework Statement



A 5.5 cm radius conducting sphere is charged until the electric field just outside its surface is 1667 V/m. What is the electric potential of this sphere, relative to infinity?

Homework Equations



V = - integral ( E (dot) dl )

The Attempt at a Solution



They only way I can think of going about this makes the potential directly related to the distance from the sphere, I know this is wrong because that would make the potential at an infinite distance go to -infinity. I am aware that for a charged sphere the potential at infinity must be 0. Is there some step I am missing that would make this field inversely proportional to the distance? I have been stuck on this one for awhile now and am not progressing...
Thanks for any help!
 
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Start by applying Gauss's law to calculate the electric field in the region outside the sphere.
 

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