Electric potential of a conducting sphere

AI Thread Summary
To find 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, one must apply Gauss's law to determine the electric field. The potential at a distance from the sphere is not directly proportional to distance, as this would incorrectly suggest that the potential approaches negative infinity at infinity. Instead, the potential at infinity is defined as zero, and the potential inside the sphere is constant. The relationship between electric field and potential must be carefully considered to avoid confusion. Understanding these principles is crucial for solving the problem correctly.
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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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