THE UNIVERSITY OF BRITISH COLUMBIA

*Physics 401 *
Assignment #
**12:**

** RADIATION ***2*

Wed. 29 Mar. 2006 - finish by Wed. 5 Apr.

Wed. 29 Mar. 2006 - finish by Wed. 5 Apr.

- (p. 450, Problem
**11.3**) -**Radiation Resistance of a Cell Phone:**

Find the**radiation resistance**of the wire joining the two ends of the oscillating electric dipole described in Section 11.1.2. (This is the resistance that would give the same average power loss - to heat - as the oscillating dipole in*fact*puts out in the form of radiation.) Show that , where is the wavelength of the radiation. For the wires in an ordinary cell phone (say,*d*=5 cm), should you worry about the radiation contribution to the total resistance? Does it matter whether your cell phone uses the 900 MHz band or the 1.9 GHz band?^{1} - (p. 454, Problem
**11.6**) -**Radiation Resistance of a Magnetic Dipole Antenna:**

Find the radiation resistance for the oscillating magnetic dipole shown in Fig. 11.8. Express your answer in terms of and*b*, and compare the radiation resistance of the*electric*dipole.^{2} - (p. 464, Problem
**11.13**) -**Nonrelativistic Bremsstrahlung Radiation:**- Suppose an electron decelerates at a constant rate
*a*from some initial velocity*v*_{0}down to zero. What fraction of its initial kinetic energy is lost to EM radiation? (The rest is absorbed by whatever mechanism keeps the acceleration constant.) Assume (nonrelativistic case) so that the Larmor formula can be used.^{3} - To get a sense of the numbers involved,
suppose the initial velocity is thermal
^{4}(around 10^{5}m/s) and the distance over which the electron decelerates to rest is 30 Å. What can you conclude about radiation losses for electrons in an ordinary conductor?

- Suppose an electron decelerates at a constant rate
**Half-Wave Antenna:**

Consider a half-wave linear antenna of length , with current , where .- Show that the linear charge density is
,
(
*i.e.*the charge density is maximum at the times when the current is zero.) - If an FM radio station broadcasts at a frequency of 10 MHz with a power of 10 kW from a half-wave antenna, how long must the antenna be? What is the current?

- Show that the linear charge density is
,
(

2006-03-23