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

Find the electric field of a uniformly polarized sphere of radius R

2. Relevant equations

[tex] V(\vec{r}) = \frac{1}{4 \pi\epsilon_{0}} \oint_{S} \frac{\sigma_{b}}{r} da' + \int_{V} \frac{\rho_{b}}{r} d\tau'[/tex]

3. The attempt at a solution

well obviously there is no volume charge density rho

but there is a surface charge density

[tex] \sigma_{b} = P \cos\theta [/tex]

now to calculate the potentail we gotta use that above formula

Suppose r > R

then

[tex] V(\vec{r}) = \frac{1}{4 \pi\epsilon_{0}} \int \frac{P \cos\theta}{r} da' [/tex]

now the squigly r is found using the cosine law right...?

[tex] r = \sqrt{R^2 + r^2 - 2Rr\cos\theta} [/tex]

and

[tex] da' = R^2 \sin\theta d\theta d\phi [/tex]

is that right???

and the limits of integrate for the theta would be from 0 to pi

and for the phi is 0 to 2pi??

thanks for your help

(o by the way how do i put the squigly r??)

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# Electric field of a uniformly polarized sphere

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