Radiation Field

Topics

• Dipole Radiation
• Larmor Formula

${\vec{E}}_{\text{rad}}(r,t)=-\frac{q}{4\pi {\epsilon }_0{c}^2}\frac{1}{r}{\vec{a}}_{\perp }(t-r/c)$

• Describes the radiated electric field due to an charge $q$ accelerating perpendicularly (${\vec{a}}_{\perp }$) to the position of measurement a distance $r$ away as a function of time
• From 3b1b video

$\vec{E}(\vec{r},t)\cong \frac{{\mu }_0}{4\pi r}[(\hat{r}\cdot \ddot{\vec{p}})\hat{r}-\ddot{\vec{p}}]=\frac{{\mu }_0}{4\pi r}[\hat{r}\times (\hat{r}\times \ddot{\vec{p}})]$

$\vec{B}(\vec{r},t)\cong -\frac{{\mu }_0}{4\pi rc}[\hat{r}\times \ddot{\vec{p}}]$