- #1

andre220

- 75

- 1

## Homework Statement

Show that the force on an elementary dipole of moment ##\mathbf{p}##, distance ##\mathbf{r}## from a point charge ##q## has components

$$\begin{eqnarray}

F_r &=& -\frac{qp\cos{\theta}}{2\pi\epsilon_0 r^3}\\

F_\theta &=& -\frac{qp\sin{\theta}}{4\pi\epsilon_0 r^3}

\end{eqnarray}$$

along and perpindicular to ##\mathbf{r}## in the plane of ##\mathbf{p}## and ##\mathbf{r}##, where ##\theta## is the angle which ##\mathbf{p}## makes with ##\mathbf{r}##.

## Homework Equations

$$\Phi(\vec{r}) = \frac{1}{4\pi\epsilon_0}\frac{\vec{p}\cdot\vec{r}}{r^3}$$

$$F = -\frac{d\Phi(\vec{r})}{dr}$$

$$\vec{p} = Q\vec{r}$$

## The Attempt at a Solution

Frankly, I do not know how to start this one. I need to find the force on the charge from the dipole. To do so, I take the derivative of ##\Phi## and find the force using Coulomb's law equation. And them decompose it in terms of ##r## and ##\theta##. Is this the right direction?