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Physics Lesson 14.5.7 - Potential of a Charged Sphere
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Welcome to our Physics lesson on Potential of a Charged Sphere, this is the seventh lesson of our suite of physics lessons covering the topic of Electric Potential, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Potential of a Charged Sphere
As explained in the previous tutorials, the electric field inside a charged sphere is zero because all charges are distributed uniformly on the surface only. This is because a sphere can naturally have only one type of extra charge, and they repel each other as far as possible as explained earlier.
Since E = ΔV / d, the potential difference inside the sphere is zero for any d as well. This means the potential inside the sphere is the same everywhere; it is equal to the potential on the outer surface, i.e.
where Q is the amount of charge the sphere carries and R is its radius.
The potential for points outside the sphere is
where r > R is the distance from the centre of sphere to the given point. In this case, the charge contained by the sphere behaves as if it was entirely concentrated at centre of the sphere. With the increase of distance from centre, the potential decreases, as electric potential and distance vary inversely.
Below, a graph expressing the relationship between electric potential and distance from the centre for a charged sphere is shown.
Example 6
A metal sphere has a charge of Q. What is the relationship between the electric potentials at point K, L, M and N shown in the figure?
Solution 6
The electric potential at any point inside the sphere and on its surface is
Here, R = 2x. Therefore, the potential at points K and L is
The points M and N are equipotential as rM = rN = 3x = 3R/2. Hence,
Therefore, we have
Or
and
You have reached the end of Physics lesson 14.5.7 Potential of a Charged Sphere. There are 8 lessons in this physics tutorial covering Electric Potential, you can access all the lessons from this tutorial below.
More Electric Potential Lessons and Learning Resources
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