**RADIATION FROM AN ANTENNA**

Our discussion of electromagnetic waves in this chapter has centered mostly on plane waves, which propagate in a single direction. In any plane perpendicular to the direction of propagation of the wave, the jj and B fields are uniform at any instant of time. Though easy to describe, plane waves are by no means the simplest to produce experimentally. Any charge or current distribution that oscillates sinusoidally with time, such as the oscillating point charge in Fig. 33 -1, produces sinusoidal electromagnetic waves, but in general there is no reason to expect them to be plane waves.

A device that uses an oscillating distribution to produce electromagnetic radiation is called an antenna. A simple example of an antenna is an oscillating electric dipole, a pair of electric charges that vary sinusoidally with time such that at any instant the two charges have equal magnitude but opposite sign. (You may want to review the definition of an electric dipole in Section 22-9.) One charge could be equal to Q sin tot and the other to -Q sin mt. An oscillating dipole antenna can be constructed in various ways, depending on frequency. One technique that works well for radio frequencies is to connect two straight conductors to the terminals of an ac source, as shown in Fig. 33-16.

The radiation pattern from an oscillating electric dipole is fairly complex, but at points far away from the dipole (compared to its dimensions and the wavelength of the radiation) it becomes fairly simple. We’ll confine our description to this far region. A key feature of the radiation in the far region is that it is not a plane wave, but a wave that

33-17 (a) An oscillating electric dipole oriented along the z-axis. The electric and magnetic fields at a point P are given by Eqs. (33-44). (b}-(f) One cycle in the production of an electromagnetic wave by an oscillating electric dipole antenna. The red curve and arrows depict the E field at points on the x-axis (where (J = trl2); the magnetic field is not shown. The figure is not to scale.

travels out radially in all directions from the source. The wave fronts are not lanes; in the far region they are expanding concentric spheres centered at the source. Figure 33-17 shows an oscillating electric dipole aligned with the z-axis, with maximum dipole moment Po. The E and ii fields at a point described by the spherical coordinates (r, 8, ¢) have the directions shown in Fig. 33-17a during half the cycle and the opposite direction during the other half. Their magnitudes in the far region.

One distinctive feature of the oscillating-dipole fields given by Eqs. (33-44) is that their magnitudes are proportional to IIr. This is in contrast to the E field of a stationary point charge or the ii field of a point charge moving with constant velocity, both of

which are proportional of l/r2. In fact, the complete expressions for the E and ii fields of an oscillating dipole also include terms that are proportional to IIr2; we haven’t included these in Eqs. (33-44), since our interest is in the behavior of the fields in the

far region, and the l/r2 terms become negligible at greater distances r from the dipole. Figure 33-18 shows a cross section of the radiation pattern at one instant. At each point, E is in the plane of the section and ii is perpendicular to that plane. The electric

field lines form closed loops, as is characteristic of induced electric fields; in the far region the electric field is induced by the variation of ii, and the magnetic field is induced by the variation of E, forming a self-sustaining wave. The field magnitudes are

greatest in the directions perpendicular to the dipole, where 8 = 1t12; there is no radiation along the axis of the dipole, where 8 = 0 or It. We saw a similar result for a single oscillating electric charge in Fig. 33-1 (Section 33-2). The key difference is that Fig.

33-18 shows only the fields that are proportional to IIr in the far region of an oscillating electric dipole, while Fig. 33-1 shows the field in the near region of a single oscillating charge; in this near region the IIr2 terms must also be included. At points very far from the oscillating dipole, E and ii are perpendicular to each other, and the direction of the Poynting vector S- (E X8)1110 is radially outward from the source. Because each field magnitude is proportional to l/r, the intensity I (the aver

is proportional to IIr2. The net average power radiated by the oscillating dipole a pherical surface of radius r centered on the dipole is the integral of the intensity over this surface. Since the area of this surface is proportional to r2, the net average power – proportional to (IIr2)(l) = 1; that is, the power radiated by the dipole in all directions is independent of r. This means that the radiated energy does not “get lost” as it spreads outward but continues on to arbitrarily great distances from the source. 1be in iry is also proportional to sin2 9, which vanishes on the axis of the dipole (9 = 0 or 9 = . 0 energy is radiated along the dipole axis. Oscillating magnetic dipoles also act as radiation sources; an example is a circular loop antenna that uses a sinusoidal current. At sufficiently high frequencies a magnetic dipole antenna is more efficient at radiating energy than is an electric dipole antenna of the same overall size.