- #1
stunner5000pt
- 1,461
- 2
Homework Statement
Find the electric field of a uniformly polarized sphere of radius R
Homework 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]
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 got to 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??)
Last edited: