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Homework Statement
Two concentric metal spherical shells of radius a and b, respectively, are separated by a weakly conducting material of conductivity sigma.
(a) If they are maintained at a potential difference V, what current flows from one to the other?
(b) What is the resistance between the shells?
(c)Notice that of b>>a the outer radius (b) is irrelevant. How do you account for that? Exploit this observation to determine the current flowing between the two metal spheres, each of radius a, immersed deep in the sea and held quite far apart, if the potential difference between the is V.
Homework Equations
Spherical Gradient:
[tex]\nabla t=\frac{\partial t}{\partial r}\hat{r}+\frac{1}{r}\frac{\partial t}{\partial\theta}\hat\theta+\frac{1}{r\sin\theta}\frac{\partial t}{\partial\phi}\hat\phi[/tex]
The rest are attached to the homework itself.
The Attempt at a Solution
Attached. I attached it having typed it up once so the prof could read it. The negative current in part a doesn't bother me as it is a vector in this case. That r in all of the answers and the negative answers in part b and c do.
Homework Statement
Homework Equations
The Attempt at a Solution
Attachments

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