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Idoubt

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## Homework Statement

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?