Calculating Total Dipole Moment of Spherical Sheet

[hansbahia]

Homework Statement

A spherical sheet of radius a has surface-charge density which depends on the polar angle θ according to the formula

σ(θ)=σ0+σ1cos(θ)

Find the total dipole moment

Homework Equations

pz=∫(dQ)z
z=rcosθ

The Attempt at a Solution

I calculated the 1st dipole moment
pz=∫∫d∅dθσ0a^3sinθcos^2θ
pz=4/3pi*a^3σ0

I'm not understanding the question, "total" dipole moment?

 

[gabbagabbahey]

I'm not understanding the question, "total" dipole moment?

When you don't understand a term, the most logical thing to do is to look it up (first try looking in your textbook & notes, and if it isn't there, then try Google, and finally just ask your instructor for clarification).

Total dipole moment just means the electric dipole moment of the entire distribution (the full vector form, not just the z-component that you get from the 2 relevant equations you posted).

 

[hansbahia]

Thanks, I figured out. I had to integrate from 0 to pi

 

[gabbagabbahey]

Thanks, I figured out. I had to integrate from 0 to pi

But do you see why the x- and y-components of the dipole moment are zero here? Getting the right answer is not the same as solving the problem.