Magnetic Dipole Radiation

$V=0$

• There’s no charge, so no potential

$\vec{A}(r,\theta ,t)=-\frac{{\mu }_0{m}_0\omega }{4\pi c}\left(\frac{\sin \theta }{r}\right)\sin [\omega (t-r/c)]\hat{\varphi }$

• Vector potential around a loop of wire with radius $b\ll r$, where $r$ is the distance from the magnetic dipole
• $\omega$ is the angular frequency of the current running through wire loop

$\vec{E}=\frac{{\mu }_0{m}_0{\omega }^2}{4\pi c}\left(\frac{\sin \theta }{r}\right)\cos [\omega (t-r/c)]\hat{\varphi }$

$\vec{B}=-\frac{{\mu }_0{m}_0{\omega }^2}{4\pi c^2}\left(\frac{\sin \theta }{r}\right)\cos [\omega (t-r/c)]\hat{\theta }$

$⟨S⟩=\left(\frac{{\mu }_0{m}_0^2{\omega }^4}{32{\pi }^2{c}^3}\right)\frac{{\sin }^2\theta }{r^2}\hat{r}$

• Same formula as in the electric dipole radiation but we replace $p_0$ with $m_0$

$⟨P⟩=\frac{{\mu }_0{m}_0^2{\omega }^4}{12\pi c^3}$

• Same formula as in the electric dipole radiation but we replace $p_0$ with $m_0$ and divide by $c^2$