Dielectric sphere in point charge electric field

AI Thread Summary
The discussion centers on calculating the electric potential inside and outside a dielectric sphere placed in the field of an external point charge. The original poster attempted to use Legendre polynomials but encountered an infinite sum that was difficult to interpret. It was clarified that while the method of images is applicable, it results in infinitely many images, complicating the solution. The conversation highlights the unexpected complexity of what seems to be a straightforward problem, noting that infinite sums are common in such calculations. Ultimately, the challenge lies in accurately representing the potential using these mathematical tools.
paweld
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I'm interested if it's possible to compute potential inside and outside
dielectric sphere (with permittivity \varepsilon_1) which is
placed in field of point charge q lying outside the sphere where
permittivity is \varepsilon_2. I've tried to solve it
using Legendre polynomilas but I obtain infinite sum which
I cannot interpretate as images (maybe I made a mistake).
So this problem cannot be solve using methods of images?
 
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Images won't work. Your LP sum is the standard solution.
 
Images work, but there are infinitly many of them!
 
Thanks for answers. It's quite strange that such apparently simple
problem has only solution in terms of infinite sum.
 
sin x is also calculated by an infinite sum.
 
indeed, for computer it doesn't matter
 

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