Dipoles

Topics

• Dipole Moment
• Multipole

$\tau =\mu E\sin \theta$

• $\tau$ is the torque on a dipole of moment $\mu$ that forms an angle $\theta$ between the dipole’s axis and the electric field $E$

$V(\vec{r})=k\frac{qd\cos \theta }{r^2}$

• $k$ is the Coloumb Constant
• $q$ is the charge of one end of the dipole (other end is $-q$)
• $d$ is the distance between the charges
• $\theta$ is the angle between the the ray going from $-q$ to $+q$ and the ray going from the center of the dipole to the point of measurement

$V(\vec{r})=k\frac{\vec{p}\cdot \hat{r}}{r^2}$

• $\vec{p}$ is the dipole moment
• $\hat{r}$ is the normalized position vector

${\vec{E}}_{\text{dip}}(r,\theta )=\frac{p}{4\pi {\epsilon }_0{r}^3}(2\cos \theta \hat{r}+\sin \theta \hat{\theta })$