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Dipole moment of a spherical shell 
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#1
Dec2111, 01:52 PM

P: 162

1. The problem statement, all variables and given/known data
I'm trying to do problem 3.28 in griffith's electrodynamics. The problem statement is, to find the dipole moment of a spherical shell with charge distribution σ = kcosθ The way I tried to do it was to use the definition of dipole moment, which griffith defines as P= ∫r σ dζ where r = position of charge w.r.t origin ( in this case R ) and dζ is volume element. The above integral gives 0 ( unless i did something stupid) I looked up the solution manual and the way it does it is to use Rcosθ ie z instead of r. Can some1 explain why this is? 


#2
Dec2311, 01:00 PM

P: 6

You should consider r in the integral as a vector. and since the charge distribution has symmetry with respect to x and y axes, we only consider z component of r which is Rcosθ. You can check x and y and make sure that they are zero.



#3
Dec2411, 09:24 AM

P: 162

I see now. My problem was that even though I looked at it as a vector, I didn't realize that the unit vector [itex]\hat{r}[/itex] itself was a function of θ and [itex]\phi[/itex] and I took it out of the integral. When i rewrite it in cartesian coordinates and do the integral for each component ( cartesian unit vectors are constant so I can take it out of the integral ) it comes out fine. But when I look at this, vector integration with spherical coordinates seems very complicated, is there an easier way than rewriting in cartesian coords and integrating?



#4
Feb2212, 03:21 PM

P: 2

Dipole moment of a spherical shell
i got confused with this problem too, thank you for taking it out.



#5
Feb2312, 02:43 AM

P: 162




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