Finding Potential Inside a Conducting Sphere

Void123
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Homework Statement



If I wanted to find the potential inside a sphere, would I be looking for the general solution (in terms of Bessel's expression) for the helmholtz equation, in spherical polar coordinates?

Also, does a 'conducting' sphere imply that there is no potential outside the sphere?



Homework Equations



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The Attempt at a Solution



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Can no one verify this for me? Have I been too ambiguous?
 
It's not really a math problem is it? Try physics.
 
Well, it is a topic addressed in the mathematical literature. But I will try your suggestion anyways. Thanks.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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