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. 

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
help_outline

Image Transcriptionclose

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

fullscreen
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.
help_outline

Image Transcriptionclose

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.

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Expert Answer

Step 1

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

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Step 2

the acceleration is.

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Step 3

Substitute the expression for the acce...

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