Essentially, I have two surfaces which I know how to find the dipole moments for. I realize that

$V_{dip}(r) = \frac{1}{4\pi \epsilon_0 r^2} \mathbf{\hat{r}} \cdot \int \mathbf{r'} \rho{(\mathbf{r'})} d\tau'$

Where $p$ is the dipole moment. Knowing this, can I assume because potential obeys superposition, so do dipole moments? Or am I missing something?



Well, I recommend always use the definition to prove things. So, take the definition of superposition: $\psi_{net} = \psi_1 + \psi_2$. So, let two potentials be $V_1$ and $V_2$. Since potentials obey superposition principle, the net potential is: $V_{net} = V_1 + V_2$.

Now.. let two dipole moments be $p_1$ and $p_2$. The net dipole: $$ p = \int_{V_1+V_2}\mathbf r'\rho(\mathbf r') d\omega = \int_{V_1}\mathbf r'\rho_1(\mathbf r') d\omega_1 + \int_{V_2}\mathbf r'\rho_2(\mathbf r') d\omega_2 = p_1 + p_2 $$

So, it obeys superposition.


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