ed and continuous (Sec. 11.9) Angular divergence, time dependence, Q-swi length (Sec. 11.10) PROBLEMS FOR CHAPTER 11 SECTION 11.2 (Radiation by Classical Charges) 11.1 • A charge q executes simple harmonic motion with po- sition x = xo sin wt. (a) Find P, the total power of the radiation emitted by this oscillating charge. (b) Show that the average power over one complete cycle is with dr/dE determined from (5 Find dr/dt when r= ag. (b) M crude approximation that dr estimate roughly how long the in from r dg to r= 0. (For mate, see Problem 11.15.) kq²w*x° (P) 2.4 11.7 Many particle accelerators and the synchrotron (Section charged particles in a circula magnetic field. The centripeta can be very large and can les by radiation, in accordance sider a 10-MeV proton in a Use the formula (11.1) to ca loss in eV/s due to radiati tried to produce electrons v gy in a circular machine o %3D 3c3 11.2 In the antenna of a TV or radio station, charges os- cillate at some frequency f and radiate electromag- netic waves of the same frequency. As a simple model of such an antenna, imagine that a single charge 9 = 250 nC is executing simple harmonic motion at mplitude 0.3 m. (1 nC = 10 to calculate %3D tion would be portions. The transition zone between the near and far fields necessarily con- at lial field. When portions of the field lines are offset from near langed position moves outward portiransverse component, as shown in Fig. 11.1(b) and (c).* While the ra- dial component of the electric field falls like 1/r it can be shown that the transverse component falls like 1/r. Consequently, at large distances it is the transverse component that dominates and carries radiated energy away from (b) the charge. The total power P radiated by any single charge q (moving nonrelativis- tically) can be shown to be ms ns 2kq a P = (c) (11.1) 3c FIGURE 11.1 ol- (a) Electric field lines from a static where a is the charge's acceleration. This formula accurately describes the charge are radial. (b) When the ply so, power radiated by any macroscopic system of moving charges. For example, in charge is given an abrupt kick to the right, changes in its electric field propagate outward at speed c distant portions of the field still point outward from the original TV or radio broadcasting, electric charges are made to oscillate inside the rods of an antenna, and the resulting radiated power is given by (11.1). (See Prob- n- lem 11.2.) Notice that the power (11.1) depends on the acceleration a. Thus a charge moving at constant velocity does not radiate. We should also mention that with an assembly of many accelerating charges, the fields produced by the uferent charges can sometimes interfere destructively, with no net radiated power. For example, consider a uniform ring of charge rotating at a constant (open circle) position. (c) The transverse disturbance linking near and far fields continues to move radially outward as the charge ats #. a- coasts forward. by er. steady current loop and does not radiate any power.

ed and continuous (Sec. 11.9) Angular divergence, time dependence, Q-swi length (Sec. 11.10) PROBLEMS FOR CHAPTER 11 SECTION 11.2 (Radiation by Classical Charges) 11.1 • A charge q executes simple harmonic motion with po- sition x = xo sin wt. (a) Find P, the total power of the radiation emitted by this oscillating charge. (b) Show that the average power over one complete cycle is with dr/dE determined from (5 Find dr/dt when r= ag. (b) M crude approximation that dr estimate roughly how long the in from r dg to r= 0. (For mate, see Problem 11.15.) kq²wx° (P) 2.4 11.7 Many particle accelerators and the synchrotron (Section charged particles in a circula magnetic field. The centripeta can be very large and can les by radiation, in accordance sider a 10-MeV proton in a Use the formula (11.1) to ca loss in eV/s due to radiati tried to produce electrons v gy in a circular machine o %3D 3c3 11.2 In the antenna of a TV or radio station, charges os- cillate at some frequency f and radiate electromag- netic waves of the same frequency. As a simple model of such an antenna, imagine that a single charge 9 = 250 nC is executing simple harmonic motion at mplitude 0.3 m. (1 nC = 10 to calculate %3D tion would be portions. The transition zone between the near and far fields necessarily con- at lial field. When portions of the field lines are offset from near langed position moves outward portiransverse component, as shown in Fig. 11.1(b) and (c). While the ra- dial component of the electric field falls like 1/r it can be shown that the transverse component falls like 1/r. Consequently, at large distances it is the transverse component that dominates and carries radiated energy away from (b) the charge. The total power P radiated by any single charge q (moving nonrelativis- tically) can be shown to be ms ns 2kq a P = (c) (11.1) 3c FIGURE 11.1 ol- (a) Electric field lines from a static where a is the charge's acceleration. This formula accurately describes the charge are radial. (b) When the ply so, power radiated by any macroscopic system of moving charges. For example, in charge is given an abrupt kick to the right, changes in its electric field propagate outward at speed c distant portions of the field still point outward from the original TV or radio broadcasting, electric charges are made to oscillate inside the rods of an antenna, and the resulting radiated power is given by (11.1). (See Prob- n- lem 11.2.) Notice that the power (11.1) depends on the acceleration a. Thus a charge moving at constant velocity does not radiate. We should also mention that with an assembly of many accelerating charges, the fields produced by the uferent charges can sometimes interfere destructively, with no net radiated power. For example, consider a uniform ring of charge rotating at a constant (open circle) position. (c) The transverse disturbance linking near and far fields continues to move radially outward as the charge ats #. a- coasts forward. by er. steady current loop and does not radiate any power.