- #1
darkpsi
- 23
- 0
Homework Statement
A sphere of radius R, centered at the origin, carries charge density
ρ(r,θ) = (kR/r2)(R - 2r)sinθ,
where k is a constant, and r, θ are the usual spherical coordinates.
Find the approximate potential for points on the z axis, far from the sphere.
Homework Equations
potential of the dipole
V(r,θ) = 1/4πεo * 1/r2 ∫ r'cosθ' ρ(r') dτ'
The Attempt at a Solution
I just want to know why I'm giving the charge density in terms of r and θ and yet I need it in terms of r'. I know that the vector r' is related to θ' by r' = rcosθ'
So I tried to say that since θ is the inclination from the xy plane and θ' is the angle between r and r' so that θ'+θ = π/2. Then that would give me
sinθ = [(π/2))-θ'] = cosθ'
Since the direction of r' is cosθ' I thought maybe I could replace r with r'?
so maybe
ρ(r',θ') = (kR/r'2)(R - 2r')cosθ' so
ρ(r') = (kR/r'2)(R - 2r') ?
PLEASE help I have a test on this tomorrow..
Last edited: