(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A dipole p is situated at thecentre of a spherical cavity of radius a in an infiite medium of relative permitivity [itex] \epsilon_r [/itex]. show that the potential in the dielectric medium is the same as would be produced by a dipole p' immersed in a continuous dielectric, where

[tex] p'=p\frac{3\epsilon_r}{2\epsilon_r +1} [/tex]

and that the field strength inside the cavity is equal to that which the dipole would produce in the absence of the dielectric, plus a uniform field E

[tex] E=\frac{2(\epsilon_r-1)}{2\epsilon_r + 1}\frac{p}{4\pi\epsilon_0a^3}. [/tex]

2. Relevant equations

3. The attempt at a solution

I am not sure at all how to approach this question. I would like to say that I would use spherical harmonics but i am not sure how to apply them in this case.

Would it be possible to say that at large distances

[tex] V_2= -\frac{p\cos\theta}{4\pi\epsilon_0\epsilon_r r^2} [/tex]

then to add then assume that outside the sphere that

[tex] V_2= -\frac{p\cos\theta}{4\pi\epsilon_0\epsilon_r r^2} + \frac{A_2\cos\theta}{r^2} [/tex]

and inisde the sphere that

[tex] V_1= B_1 r \cos\theta + \frac{B_2\cos\theta}{r^2} [/tex]

and then solve the problem using the boundary conditions for tangential E and perpendicular D?

I am really unsure of how to solve this and any help will be greatly appreciated.

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# Homework Help: Dipole in a dielectric medium

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