Register to reply

Dipole moment of a spherical shell

by Idoubt
Tags: dipole, moment, shell, spherical
Share this thread:
Dec21-11, 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?
Phys.Org News Partner Science news on
FIXD tells car drivers via smartphone what is wrong
Team pioneers strategy for creating new materials
Team defines new biodiversity metric
Dec23-11, 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.
Dec24-11, 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 co-ordinates 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 co-ordinates seems very complicated, is there an easier way than rewriting in cartesian co-ords and integrating?

Feb22-12, 03:21 PM
P: 2
Dipole moment of a spherical shell

i got confused with this problem too, thank you for taking it out.
Feb23-12, 02:43 AM
P: 162

Register to reply

Related Discussions
Moment of inertia of spherical shell Introductory Physics Homework 1
Dipole moment of non-conducting spherical shell Advanced Physics Homework 1
Potential inside a grounded spherical conducting shell due to point dipole Introductory Physics Homework 23
Moment of inertia of spherical shell Introductory Physics Homework 2
Moment of inertia of spherical shell Introductory Physics Homework 2