Electric potential of a conducting sphere

Then, use the relationship between electric field and electric potential to find the potential at a distance r from the sphere. Finally, take the limit as r approaches infinity to find the potential at infinity, which must be 0 for a charged sphere. In summary, to find the electric potential of a 5.5 cm radius conducting sphere with an electric field just outside its surface of 1667 V/m, apply Gauss's law and use the relationship between electric field and potential, taking the limit as the distance approaches infinity to find the potential at infinity.
  • #1
elyons
10
1

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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  • #2
Start by applying Gauss's law to calculate the electric field in the region outside the sphere.
 

FAQ: Electric potential of a conducting sphere

What is electric potential?

Electric potential is a measure of the electrical potential energy per unit charge at a specific point in space.

How is electric potential calculated?

For a conducting sphere, the electric potential can be calculated by dividing the charge on the sphere by its capacitance.

What is the difference between electric potential and electric field?

Electric potential is a scalar quantity that represents the potential energy per unit charge, while electric field is a vector quantity that represents the force per unit charge. Electric potential is dependent on the source charge, while electric field is dependent on both the source charge and the test charge.

How does the electric potential of a conducting sphere vary with distance?

The electric potential of a conducting sphere is inversely proportional to the distance from the center of the sphere. As the distance increases, the electric potential decreases.

Can the electric potential of a conducting sphere be negative?

Yes, the electric potential can be negative if the sphere has a net negative charge. This means that the electric potential energy of a negatively charged object would decrease as it moves closer to the sphere.

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