A Jackson Sec 2.6 on "general solution" of charge near sphere

AI Thread Summary
Section 2.6 of Jackson's E&M discusses the interaction between a point charge and a sphere, but it does not pertain to a conducting sphere, as the potential varies with azimuth and polar angle. The sphere in question is likely a non-interacting sphere, which raises concerns about its practical relevance in real-world applications. The Dirichlet Green's function mentioned is related to the potential of a point charge outside a conducting sphere, but the example provided seems to lack utility. The discussion emphasizes that the specific type of sphere is less important than understanding the principles of Green's functions. Ultimately, the section may be seen as an abstract exercise rather than a practical scenario.
ForgetfulPhysicist
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Hi , I'd like a little bit of clarification about Section 2.6 from Jackson's classic book on E & M.

Section 2.6 starts out with the problem of a "conducting sphere" near a point charge, but then it confusingly veers away to a problem where potential is prescribed to vary with azimuth and polar angle. So my question is: can somebody verify that the solution at the end of Section 2.6 is NOT for a conducting sphere? After all, a conducting sphere would NOT have potential varying in the azimuth etc...

Further, if it's NOT a conducting sphere then what is the interaction between the "nearby point charge" and the sphere? Is it a dielectric sphere? Is it a completely non-interacting sphere?
 
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The sphere in 2.6 is not a conducting sphere, but the Dirichlet Green's function is the potential given by a point charge outside a conducting sphere.
 
Please continue on to answer my follow on questions: "if it's NOT a conducting sphere then what is the interaction between the "nearby point charge" and the sphere? Is it a dielectric sphere? Is it a completely non-interacting sphere?"
 
It seems the answer is "it's a completely non-interacting sphere near a point charge"... which seems to be a very useless, rarely occurring, seldom-real-world-application, mathterbation example for Jackson to spend our time on.
 
For the Dirchlet condition, i.e., ##G(\vec{x},\vec{x}')=0## for ##\vec{x}' \in S## (where ##S## is the surface under consideration, i.e., in this case the sphere), the Green's function is formally the electrostatic potential ##\phi(\vec{x}')## for a unit charge located in ##\vec{x}## at presence of a conducting "grounded" surface ##S##. For a sphere it can be determined using the method of image charges.
 
"Is it a dielectric sphere? Is it a completely non-interacting sphere?"
It doesn't matter what kind of sphere it is. Read Jackson's section on Green's functions.
 

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