a dipole antenna
A dipole antenna is the workhorse that turns an oscillating current in a wire into radio waves streaming into space — and, run in reverse, catches passing waves and turns them back into a current. It is the practical embodiment of electric dipole radiation: an oscillating dipole you can actually build and feed.
In the simplest form, two collinear conducting rods are driven at their inner ends by an alternating source. The current is not uniform — it must vanish at the open ends and, for the popular half-wave dipole (total length equal to lambda/2), forms a standing half-sine along the wire. The antenna's ability to radiate is captured by its radiation resistance R_rad, defined so that the time-averaged radiated power is P = (1/2) I_0^2 R_rad; for a short dipole R_rad = 790 (d/lambda)^2 ohms, while the resonant half-wave dipole has R_rad about 73 ohms. The far-field pattern is doughnut-shaped, strongest broadside and null along the wire — exactly the sin(theta) dependence of an electric dipole.
Radiation resistance is real in the sense that the source cannot tell it apart from ordinary ohmic resistance — both drain power from the feed — but here the 'lost' power is not heat, it is the useful radiated wave. Matching a transmitter to the antenna's roughly 73-ohm resonant resistance (hence 75-ohm coaxial cable) is central to real antenna engineering. Longer antennas or arrays sharpen the pattern by bringing in higher multipoles and interference between elements.
For a broadcast at wavelength lambda, a half-wave dipole is physically about lambda/2 long. For FM radio near 100 MHz, lambda is about 3 m, so the antenna is roughly 1.5 m — the size of a real rooftop or car aerial. Its radiation resistance is about 73 ohms, which is why feedlines are made near 75 ohms.
A half-wave dipole is ~lambda/2 long, with ~73 ohms radiation resistance and a sin(theta) doughnut pattern.
Radiation resistance is not heat dissipation — it represents power carried off as radiation, though it drains the feed just like a resistor. The current on a real dipole is not uniform; it falls to zero at the open ends, which is why the half-wave standing-wave pattern matters.