-\begin{problem*}{23.1}
+\begin{problem*}{23.1} % induction
A flat loop of wire consisting of a single turn of cross-sectional
area $A=8.00\U{cm$^2$}$ is perpendicular to a magnetic field that
increases uniformly in magnitude from $B_i = 0.500\U{T}$ to $B_f =
2.50\U{T}$ in $1.00\U{s}$. What is the resulting induced current if
the loop has a resistance of $R = 2.00\Omega$.
-\end{problem*} % problem 23.1
+\end{problem*}
\begin{solution}
By Faraday's law
-\begin{problem*}{23.2}
+\begin{problem*}{23.2} % induction
An $N = 25$ turn circular coil of wire has diameter $d = 1.00\U{m}$.
It is placed with it's axis along the direction of the Earth's
magnetic field of $B = 50.0\U{$\mu$T}$, and then in $t = 0.200\U{s}$
it is flipped 180\dg. An average emf of what magnitude is generated
in the coil?
-\end{problem*} % problem 23.2
+\end{problem*}
\begin{solution}
The flux before the flip is
-\begin{problem*}{23.6}
+\begin{problem*}{23.6} % transformers
A coil of $N=15$ turns and radius $R=10.0\U{cm}$ surrounds a long
solenoid of radius $r=2.00\U{cm}$ and $n=1.00\E{3}\U{turns/m}$
(Fig.~P23.6). The current in the solenoid changes as
$I=(5.00\U{A})\sin(120t)$. Find the induced emf in the $15$ turn coil
as a function of time.
-\end{problem*} % problem 23.6
+\end{problem*}
\begin{solution}
Because the solenoid is long, we can pretend it is infinite, so all
-\begin{problem*}{23.7}
+\begin{problem*}{23.7} % induction
An $N=30$ turn circular coil of radius $r = 4.00\U{cm}$ and resistance
$R = 1.00\Omega$ is placed in a magnetic field directed perpendicular
to the plane of the coil. The magnitude of the magnetic field varies
with time according to $B = 0.0100t + 0.0400t^2$, where $t$ is in
seconds and $B$ is in Tesla. Calculate the induced emf in the coil
at $t= 5.00\U{s}$.
-\end{problem*} % problem 23.7
+\end{problem*}
\begin{solution}
The magnetic flux through the loop is
-\begin{problem*}{23.10}
+\begin{problem*}{23.10} % induction
A piece of insulated wire is shaped into a figure eight as shown in
Figure P23.10. The radius of the upper circle is $r_s = 5.00\U{cm}$
and that of the lower circle is $r_b = 9.00\U{cm}$. The wire has a
two circles, in the direction shown. The magnetic field is increasing
at a constant rate of $dB/dt = 2.00\U{T/s}$. Find the magnitude and
direction of the induced current in the wire.
-\end{problem*} % problem 23.10
+\end{problem*}
\begin{solution}
Pick a direction for the current to be counterclockwise in the bottom
-\begin{problem*}{23.12}
+\begin{problem*}{23.12} % rail guns
Consider the arrangement shown in Figure P23.12. Assume that $R =
6.00\Omega$, $l = 1.20\U{m}$, and a uniform $B=2.50\U{T}$ magnetic
field is directed into the page. At what speed should the bar be
-\begin{problem*}{23.13}
+\begin{problem*}{23.13} % rail guns
Figure P23.12 shows a top view of a bar that can slide without
friction. The resistor is $R = 6.00\Omega$, and a $B = 2.50\U{T}$
magnetic field is directed perpendicularly downward, into the paper.
\Part{a} Calculate the applied force required to move the bar to the
right at a constant speed $v = 2.00\U{m/s}$.
\Part{b} At what rate is energy delivered to the resistor?
-\end{problem*} % problem 23.13
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{23.22}
+\begin{problem*}{23.22} % induction
A rectangular coil with resistance $R$ has $N$ turns, each of length
$l$ and width $w$ as shown in Figure P23.22. The coil moves in a
uniform magnetic field \vect{B} with constant velocity $v$. What are
-the magnitude and direction of the total magnetic force on the coild
+the magnitude and direction of the total magnetic force on the coil
as it
\Part{a} enters,
\Part{b} moves within, and
\Part{c} leaves
the magnetic field.
-\end{problem*} % problem 23.22
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{23.53}
+\begin{problem*}{23.53} % cyclotrons
A particle with a mass of $m = 2.00\E{-16}\U{kg}$ and a charge of $q =
30.0\U{nC}$ starts from rest, is accelerated by a strong electric
field, and is fired from a small source inside a region of uniform
\Part{a} Calculate the speed of the particle.
\Part{b} Calculate the potential difference through which the particle
accelerated inside the source.
-\end{problem*} % problem 23.53
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{23.64}
+\begin{problem*}{23.64} % inductor energy
A novel method of storing energy has been proposed. A huge,
underground, superconducting coil, $d = 1.00\U{km}$ in diameter, would
be fabricated. It would carry a maximum current of $I=50.0\U{kA}$
what would be the total energy stored?
\Part{b} What would be the compressive force per meter length acting
between two adjacent windings $r = 0.250\U{m}$ apart?
-\end{problem*} % problem 23.64
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{24.7}
+\begin{problem*}{24.7} % EM waves
Figure 24.3 shows a plane electromagnetic sinosoidal wave propogating
in the $x$ direction. Suppose the wavelength is $50.0\U{m}$ and the
electric field vibrates in the $xy$ plane with an amplitude of
\begin{equation}
B = B_\text{max}\cos(kx-\omega t)
\end{equation}
-\end{problem*} % problem 24.7
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{24.8}
+\begin{problem*}{24.8} % EM waves
In SI units, the electric field in an electromagnetic wave is described by
\begin{equation}
E_y = 100\sin(1.00\E{7}x - \omega t)
Find \Part{a} the amplitude of the corresponding magnetic field
oscillations, \Part{b} the wavelength $\lambda$, and \Part{c} the
frequency $f$.
-\end{problem*} % problem 24.8
+\end{problem*}
\begin{solution}
\Part{a}
\newcommand{\Bm}{B_\text{max}}
\newcommand{\ctrig}{\cos(kx-\omega t)}
\newcommand{\strig}{\sin(kx-\omega t)}
-\begin{problem*}{24.9}
+\begin{problem*}{24.9} % EM waves, Maxwell's equations
Verify by substitution that the following equations are solutions to
Equations 24.15 and 24.16 respectively:
\begin{align}
\npderiv{2}{x}{E} &= \epsilon_0\mu_0 \npderiv{2}{t}{E} \tag{24.15} \\
\npderiv{2}{x}{B} &= \epsilon_0\mu_0 \npderiv{2}{t}{B} \tag{24.16}
\end{align*}
-\end{problem*} % problem 24.9
+\end{problem*}
\begin{solution}
This is just an excercise in partial derivatives.
-\begin{problem*}{24.22}
+\begin{problem*}{24.22} % power <-> EM fields
An AM radio station broadcasts isotropically (equally in all
directions) with an average power of $4.00\U{kW}$. A dipole recieving
antenna $65.0\U{cm}$ long is at a location $4.00\U{miles}$ from the
transmitter. Compute the amplitude of the emf that is induced by this
signal between the ends of the recieving antenna.
-\end{problem*} % problem 24.22
+\end{problem*}
\begin{solution}
To find the signal intensity at our antenna, we note that the power
-\begin{problem*}{24.25}
+\begin{problem*}{24.25} % Poynting vector, power <-> EM fields
The filament of an incandescent lamp has a $150\U{\Ohm}$ resistance
and carries a direct current of $1.00\U{A}$. The filament is
$8.00\U{cm}$ long and $0.900\U{mm}$ in radius. \Part{a} Calculate
-thte Poynting vector at the surface of the filament, associated with
+the Poynting vector at the surface of the filament, associated with
the static electric field producing the current and the curret's
static magnetic field. \Part{b} Find the magnitude of the static
electric and magnetic fields at the surface of the filament.
-\end{problem*} % problem 24.25
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem}
+\begin{problem} % thin film interference
An oil film ($n = 1.5$) floats on the surface of a bowl of water. The
film is illuminated by a white light placed directly above the bowl.
Red light at $\lambda = 650\U{nm}$ is the most strongly reflected
-\begin{problem*}{28.4}
+\begin{problem*}{28.4} % photon energy
Calculate the energy, in electron volts, of a photon whose frequency
is \Part{a} $620\U{THz}$, \Part{b} $3.10\U{GHz}$, and \Part{c}
$46.0\U{MHz}$. \Part{d} Determine the corresponding wavelengths for
these photons and state the classification of each on the
electromagnetic spectrum.
-\end{problem*} % problem 28.4
+\end{problem*}
\begin{solution}
\begin{center}
-\begin{problem*}{28.6}
+\begin{problem*}{28.6} % photon energy
The average threshold of dark-adapted (scotopic) vision is
$4.00\E{-11}\U{W/m$^2$}$ at a central wavelength of $500\U{nm}$. If
light having this intensity and wavelength enters the eye and the
pupil is open to its maximum diameter of $8.50\U{mm}$, how many
photons per second enter the eye?
-\end{problem*} % problem 28.6
+\end{problem*}
\begin{solution}
The total power into the eye is
-\begin{problem*}{28.9}
+\begin{problem*}{28.9} % photoelectric effect
Molybdenum has a work function of $4.20\U{eV}$. \Part{a} Find the
cutoff wavelength and cutoff frequency for the photoelectic
effect. \Part{b} What is the stopping potential if the incident light
has a wavelength of $180\U{nm}$?
-\end{problem*} % problem 28.9
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{28.10}
+\begin{problem*}{28.10} % photoelectric effect
Electrons are ejected from a metallic surface with speeds ranging up
to $4.60\E{5}\U{m/s}$ when light with a wavelength of $625\U{nm}$ is
used. \Part{a} What is the work function of the surface? \Part{b}
What is the cutoff frequency for this surface?
-\end{problem*} % problem 28.10
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{28.13}
+\begin{problem*}{28.13} % photoelectric effect
An isolated copper sphere of radius $5.00\U{cm}$, initially uncharged,
is illuminated by ultraviolet light of wavelength $200\U{nm}$. What
charge will the photoelectric effect induce on the sphere? The work
function for copper is $4.70\U{eV}$.
-\end{problem*} % problem 28.13
+\end{problem*}
\begin{solution}
As light lands on the sphere, electrons are blasted off into oblivion.
-\begin{problem*}{28.14}
+\begin{problem*}{28.14} % photon energy
Calculate the energy and momentum of a photon of wavelength $700\U{nm}$.
-\end{problem*} % problem 28.14
+\end{problem*}
\begin{solution}
You should be familiar with these equations by now (after our time
-\begin{problem*}{28.15}
+\begin{problem*}{28.15} % Compton effect
X-rays having an energy of $300\U{keV}$ undergo Compton scattering
from a target. The scattered rays are detected at $37.0\dg$ relative
to the incident rays. Find \Part{a} the Compton shift at this
angle, \Part{b} the energy of the scattered x-ray, and \Part{c} the
energy of the recoiling electron.
-\end{problem*} % problem 28.15
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{28.16}
+\begin{problem*}{28.16} % Compton effect
A $0.110\U{nm}$ photon collides with a stationary electron. After
the collision, the electron moves forward and the photon recoils
backward. Find the momentum and the kinetic energy of the electron.
-\end{problem*} % problem 28.16
+\end{problem*}
\begin{solution}
The photon scatters by $180\dg$, so from the Compton shift equation
-\begin{problem}
+\begin{problem*}{28.25} % diffraction, resolution
The resolving power of a microscope depends on the wavelength of light
used. If one wished to ``see'' an atom, a resolution of approximately
$1.00\E{-11}\U{\m}$ would be required. \Part{a} If electrons are used
-(in an electron microscope), what minimum kinetic energy is required for the electrons? \Part{b} If photons are used, what minimum photon energy is needed to obtain the required resolution?
-\end{problem} % Problem 28.25
+(in an electron microscope), what minimum kinetic energy is required
+for the electrons? \Part{b} If photons are used, what minimum photon
+energy is needed to obtain the required resolution?
+\end{problem*}
\begin{solution}
\Part{a}
-\begin{problem*}{28.56}
+\begin{problem*}{28.56} % photoelectric effect
Figure P28.56 shows the stopping potential versus the incident photon
-frequency for the photoelectric effect for sodupm. Use the graph to
+frequency for the photoelectric effect for sodium. Use the graph to
find \Part{a} the work function, \Part{b} the ratio $h/e$,
and \Part{c} the cutoff wavelength. The data are taken from
R.A.~Millikan, \emph{Physical Review} 7:362 (1916).
-\begin{problem*}{28.57}
+\begin{problem*}{28.57} % photoelectric effect
The following table shows data obtained in a photoelectric
experiment. \Part{a} Using these data, make a graph similar to Active
Figure 28.9 that plots as a straight line. From the graph,
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