Dipoles

#Physics

Topics

• Dipole Moment
• Multipole

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

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

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

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

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

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

$\displaystyle \vec{E}{\text{dip}}(r,\theta)=\frac{p}{4\pi {\varepsilon}{0}r^{3}}(2\cos \theta \hat{r}+\sin \theta \hat{\theta})$