Radiation Field

#Physics

Topics

• Dipole Radiation
• Larmor Formula

$\displaystyle \vec{E}{\text{rad}}(r,t)=-\frac{q}{4\pi {\varepsilon}{0}c^{2}} \frac{1}{r}\vec{a}_{\perp}(t-r/c)$

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

$\displaystyle \vec{E}(\vec{r},t)\cong \frac{{\mu}{0}}{4\pi r}[(\hat{r}\cdot \ddot{\vec{p}})\hat{r}-\ddot{\vec{p}}]=\frac{{\mu}{0}}{4\pi r}[\hat{r}\times (\hat{r}\times \ddot{\vec{p}})]$

$\displaystyle \vec{B}(\vec{r},t)\cong -\frac{{\mu}_{0}}{4\pi rc}[\hat{r}\times \ddot{\vec{p}}]$