In front of an indefinite conducting plane connected to ground and at a distance $d$ of it we locate an electric dipole with dipolar moment $\textbf{p}$ parallel to the plane. What electric field acts on the dipole? Does the force which acts on the dipole tend to push it away or bring it closer to the plane?
I know that the dipole induced an image dipole at a distance $d$ but symmetrically respect to the real. Moreover, this induced dipole has inverted orientation. However, I don't know how to interpret that the electric field acts on the dipole.
Note: The electric field of an ideal dipole is
$$\textbf{E}=\frac{1}{4\pi\varepsilon_0}\left[\frac{3(\textbf{p}\cdot \textbf{r})\textbf{r}}{r^5}-\frac{\textbf{p}}{r^3}\right].$$
Answer
When you make a diagram that shows the image dipole, you will see that the negative image charge is a little closer to the positive real charge, and vice versa.
There will be some repulsive and some attractive forces - but the closer charges will have the greater effect. The net result is an attraction.
You can compute this exactly by writing the force for each pair of charges explicitly (four interactions); you should find that you have to use first order expansion of your terms, then be careful not to cancel things that are "almost, but not quite, equal".
No comments:
Post a Comment