Force on a charge from an induced dipole


by Yitzach
Tags: dipole moment, electric field, electric force, induced dipole, polarization
Yitzach
Yitzach is offline
#1
Dec6-09, 11:38 PM
P: 61
1. The problem statement, all variables and given/known data
A point charge q is situated a large distance r from a neutral atom of polarizability [tex]\alpha[/tex]. Find the force of attraction between them.

2. Relevant equations
[tex]\vec{E}_{mono}(r)=\frac{q}{4\pi\epsilon_0r^2}\hat{r}[/tex]
[tex]\vec{E}_{dip}(r,\theta)=\frac{p}{4\pi\epsilon_0r^3}(2\cos\theta\hat{r}+ \sin\theta\hat{\theta})[/tex]
[tex]\vec{p}=\alpha\vec{E}[/tex]

3. The attempt at a solution
[tex]\vec{E}_{mono}(r)=\frac{q}{4\pi\epsilon_0r^2}\hat{r}[/tex]
[tex]\vec{p}=\alpha\vec{E}[/tex]
[tex]\vec{p}=\frac{\alpha q}{4\pi\epsilon_0r^2}\hat{r}[/tex]
[tex]\vec{E}_{dip}(r,\theta)=\frac{p}{4\pi\epsilon_0r^3}(2\cos\theta\hat{r}+ \sin\theta\hat{\theta})[/tex]
[tex]\vec{E}_{dip}(r,\pi)=\frac{\alpha q}{16\pi^2\epsilon^2_0r^5}(-2\hat{r})[/tex]
[tex]\vec{E}_{dip}(r,\pi)=-\frac{\alpha q}{8\pi^2\epsilon^2_0r^5}\hat{r}[/tex]
[tex]\vec{F}=q\vec{E}[/tex]
[tex]\vec{F}=-\frac{\alpha q^2}{8\pi^2\epsilon^2_0r^5}\hat{r}[/tex]

The result I got was unexpected because that is a repulsive force.
Do I need to go about a longer way or did I mess it up somewhere?
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