Asymptotic properties in the Zones

In the near zone we get:

$$\vB = \mu_0\vH = \frac{i\omega\mu_0}{4\pi}(\hn \times \vp) \frac{1}{r^2}$$ (13.49)

$$\vE = \frac{1}{4\pi \epsilon_0}[3\hn(\hn \cdot \vp) - \vp] \frac{1}{r^3}$$ (13.50)

and can usually neglect the magnetic field relative to the electric field (it is smaller by a factor of $kr << 1$ ). The electric field is that of a ``static'' dipole (J4.13) oscillating harmonically.

In the far zone we get:

$$\vB = \mu_0 \vH = \frac{ck^2\mu_0}{4\pi}\left(\hn \times \vp\right) \frac{e^{ikr}}{r}$$ (13.51)

$$\vE = \frac{ic}{k}\curl \vB = c \left(\vB \times \hn\right).$$ (13.52)

This is transverse EM radiation. Expanded about any point, it looks just like a plane wave (which is how ``plane waves'' are born!). We are most interested, as you know, in the radiation zone and so we will focus on it for a moment.