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Dielectric Sphere in Field of a Point Charge 
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#1
Sep808, 01:31 PM

P: 203

Hi,
I have derived the electric potential equations inside and outside the sphere due to a point charge [tex]q[/tex] placed a distance [tex]b[/tex] way from the sphere's center. The potentials are given by: [tex]\Phi_{in}(r,\theta) = \sum^{\infty}_{n=0} A_{n}r^{n}P_{n}(cos\theta) [/tex] and [tex]\Phi_{out}(r,\theta) = \sum^{\infty}_{n=0} \frac{kr^{n}}{b^{n+1}} + \sum^{\infty}_{n=0}\frac{B_{n}}{r^{n+1}}P_{n}(cos\theta) [/tex] where [tex]k=\frac{q}{4\pi\epsilon_{0}}[/tex] and [tex]P_{n}[/tex]  are the Legendre polynomials I have calculated the the constants [tex]A_{n}[/tex] and [tex]B_{n}[/tex] according to the usual boundary conditions. Unfortunately, almost non of them are equal to zero unlike the the case of a 'sphere in a uniform field'. Is there any way of truncating these infinite sums to end up with something nice and clean? 


#2
Sep808, 05:04 PM

Sci Advisor
P: 1,260

No. It is an infinite series.



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