Dielectric Sphere in Field of a Point Charge

by Apteronotus
Tags: dielectric sphere, point charge
Apteronotus is offline
Sep8-08, 01:31 PM
P: 196
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]\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]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?
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
clem is offline
Sep8-08, 05:04 PM
Sci Advisor
P: 1,250
No. It is an infinite series.

Register to reply

Related Discussions
electric field of a line charge and point charge Introductory Physics Homework 14
Point Charge around a sphere Advanced Physics Homework 2
Why is E field zero in a sphere of charge? Advanced Physics Homework 2
One E field eq in/outside sphere of charge? Classical Physics 4
Point charge in a hollow sphere Introductory Physics Homework 1