What is the potential of a thin spherical shell?
I have a sphere of radius 10 cm with charge 6 μC and I need to find the Potential at the center of the sphere. To me it seems like the potential would not be zero at the center of the sphere because there is no electric field! Why is this not right though?
Answer
When we talk about electric potential, we are actually talking about the potential difference between two points in space. In other words, a single value for the potential doesn't mean anything on its own; only the difference is meaningful to us!
We have to define where our potential is zero before we can talk about the potential at other locations. Typically, we define the potential to be zero infinitely far away. If this is the case, as it is for this problem, to find the potential everywhere else we have to integrate the electric field up starting from infinity. Fortunately, this has already been done for you in one of your formulas:
V = kQ/r
This formula is valid for a point charge, but can you also use it in this problem? Outside the symmetric spherical shell, the electric field looks the same as a point charge, so this formula is actually valid for r > R where R is the radius of the shell. Once you find the potential right outside of the shell, it's up to you to think about how the potential does or doesn't change as you go to the center of the sphere.
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When we talk about electric potential, we are actually talking about the potential difference between two points in space. In other words, a single value for the potential doesn't mean anything on its own; only the difference is meaningful to us!
We have to define where our potential is zero before we can talk about the potential at other locations. Typically, we define the potential to be zero infinitely far away. If this is the case, as it is for this problem, to find the potential everywhere else we have to integrate the electric field up starting from infinity. Fortunately, this has already been done for you in one of your formulas:
V = kQ/r
This formula is valid for a point charge, but can you also use it in this problem? Outside the symmetric spherical shell, the electric field looks the same as a point charge, so this formula is actually valid for r > R where R is the radius of the shell. Once you find the potential right outside of the shell, it's up to you to think about how the potential does or doesn't change as you go to the center of the sphere.