Dipole antenna

The simplest source studied by Hertz is the dipole antenna: a length of conducting wire of length $L$ fed at its centre by an alternating generator that makes the current oscillate at frequency $f$. For a dipole that radiates efficiently, the optimal length is $L \approx \lambda/2$, with $\lambda = c/f$ the associated wavelength.

Vertical dipole antenna: the alternating generator at the centre makes the current $i(t)$ oscillate; the wave fronts radiate outwards concentrically.

Far from the antenna (far field, $r \gg \lambda$) the magnitude of the wave decreases as $1/r$, so the intensity decreases as $1/r^2$ — as for an isotropic point source, but with a torus-shaped directionality: maximum in the equatorial plane, zero along the dipole’s axis. The polarisation of the emitted electric field is parallel to the antenna’s axis: a vertical antenna emits waves with $\vec{E}$ vertical.

Example — FM and WiFi antennas

An FM radio station at $f = 100$ MHz has $\lambda = c/f = 3$ m: an optimal dipole is about $1{,}5$ m long, exactly the size typically seen on masts. WiFi at $f = 2{,}4$ GHz has $\lambda \approx 12{,}5$ cm: the antenna is about $6$ cm long and fits entirely inside the router. A mobile phone at $f \approx 1{,}8$ GHz ($\lambda \approx 17$ cm) has an antenna a couple of centimetres long. It is always the same physics: everything is fixed by the wavelength (Bloomfield 2016).

Tesla's "wireless light bulb"

In 1891 Nikola Tesla showed gas tubes that lit up in his hand without wires: the EM field of a high-frequency coil ionised the gas at a distance. The same idea is exploited today by the wireless charging of smartphones: an antenna in the base generates an oscillating magnetic field that induces a current in a receiving antenna inside the phone’s casing — a miniature version of Hertz’s experiment.

In summary

Accelerated charge $\to$ EM wave. Dipole antenna of length $\lambda/2$, with $\vec{E}$ parallel to the axis and intensity $\propto 1/r^2$.

Links

Topics: Electromagnetic waves Concepts: Electromagnetic wave · Polarisation and Malus’s law · Intensity of a wave

Related exercises: Problem — TV antennas and polarisation · Problem — Crossed polarisers · Problem — Crossed polarisers with one in between