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Suppose the potential V0(?) at the surface of a sphere is

Chapter 3, Problem 20P

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QUESTION:

Problem 20P

Suppose the potential V0(θ) at the surface of a sphere is specified, and there is no charge inside or outside the sphere. Show that the charge density on the sphere is given by

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QUESTION:

Problem 20P

Suppose the potential V0(θ) at the surface of a sphere is specified, and there is no charge inside or outside the sphere. Show that the charge density on the sphere is given by

ANSWER:

Solution 20P

Step 1 of 3:

Consider a sphere having no charges on its inside and the outside. The radius of the sphere is R. The potential at the surface of the sphere is also given. We are going to prove the expression for the charge density as given in the problem. The potential at the surface of the sphere is V0(θ).

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