# ed and continuous (Sec. 11.9)Angular divergence, time dependence, Q-swilength (Sec. 11.10)PROBLEMS FOR CHAPTER 11SECTION 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 theradiation emitted by this oscillating charge. (b) Showthat the average power over one complete cycle iswith dr/dE determined from (5Find dr/dt when r= ag. (b) Mcrude approximation that drestimate roughly how long thein from r dg to r= 0. (Formate, see Problem 11.15.)kq²w*x°(P)2.411.7 Many particle acceleratorsand the synchrotron (Sectioncharged particles in a circulamagnetic field. The centripetacan be very large and can lesby radiation, in accordancesider a 10-MeV proton in aUse the formula (11.1) to caloss in eV/s due to radiatitried to produce electrons vgy in a circular machine o%3D3c311.2 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 modelof such an antenna, imagine that a single charge9 = 250 nC is executing simple harmonic motion atmplitude 0.3 m. (1 nC = 10to calculate%3Dtion would be portions. The transition zone between the near and far fields necessarily con-atlial field. Whenportions of the field lines are offset from nearlanged position moves outwardportiransverse 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 thetransverse component falls like 1/r. Consequently, at large distances it is thetransverse 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 bemsns2kq aP =(c)(11.1)3cFIGURE 11.1ol-(a) Electric field lines from a staticwhere a is the charge's acceleration. This formula accurately describes the charge are radial. (b) When theplyso,power radiated by any macroscopic system of moving charges. For example, in charge is given an abrupt kick tothe right, changes in its electric fieldpropagate outward at speed cdistant portions of the field stillpoint outward from the originalTV or radio broadcasting, electric charges are made to oscillate inside the rodsof 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 acharge moving at constant velocity does not radiate. We should also mentionthat with an assembly of many accelerating charges, the fields produced by theuferent charges can sometimes interfere destructively, with no net radiatedpower. For example, consider a uniform ring of charge rotating at a constant(open circle) position. (c) Thetransverse disturbance linking nearand far fields continues to moveradially outward as the chargeats#.a-coasts forward.byer.steady current loop and does not radiate any power.

Question
Asked Jan 14, 2020
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How might I be able to answer Problem 11.1? I could some kind of integral in order to find the average P for part B, but I'm not sure. This section is in a chapter named "Atomic Transitions and Radiation," and is under quantum mechanics.

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## Expert Answer

Step 1

the expression for the power radiated by the single charge is,

Step 2

the acceleration is.

Step 3

Substitute the expression for the acce...

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