- #1

- 458

- 1

[tex]

\Phi (\mathbf{r}) = \frac {1} {4\pi\epsilon_0 r^2} (\mathbf{p}\cdot\hat{\mathbf{r}})

[/tex]

E is the electric field

r,

*r*, r\hat are as above

p is the (vector) dipole moment

e0 is the primitivity of free space

To find the electric field I have to take the derivative as follows.

[tex]

\mathbf{E} = - \nabla \Phi

[/tex]

The derivative looks like this:

[tex]

\mathbf{E} = \frac {1} {4\pi\epsilon_0 r^3} \left(3(\mathbf{p}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{p}\right)

[/tex]

I'm confused by the vector notation. Why do I have r\hat multiplied by r\hat? Why is the electric field simply not

[tex]

\Phi (\mathbf{r}) = \frac {1} {2\pi\epsilon_0 r^3} (\mathbf{p}\cdot\hat{\mathbf{r}})

[/tex]