-\begin{problem*}{27.22}
+\begin{problem*}{27.22} % cyclotrons
In an experiment with cosmic rays, a verticle beam of particles that
have charge of magnitude $3e$ and mass $12$ times the proton mass
enters a uniform horizontal magnetic field of $0.250\U{T}$ and is bent
-\begin{problem*}{27.30}
+\begin{problem*}{27.30} % Lorentz force
A particle with initial velocity $\vect{v}_0=5.85\E{3}\U{m/s}\jhat$
enters a region of uniform electric and magnetic fields. The magnetic
field in the region is $\vect{B}=-(1.35\U{T})\khat$. Calculate the
-\begin{problem*}{27.35}
+\begin{problem*}{27.35} % magnetic force on wires
A long wire carrying $4.50\U{A}$ of current makes two $90\dg$ bends,
as shown in Fig.~27.49. The bent part of the wire passes through a
uniform $0.240\U{T}$ magnetic field direceted as shown in the figure
-\begin{problem*}{27.39}
+\begin{problem*}{27.39} % rail guns
A thin, $50.0\U{cm}$ long metal bar with mass $750\U{g}$ rests on, but
is not attached to, two metallic supports in a uniform $0.450\U{T}$
magnetic field, as shown in Fig.~27.51. A battery and a
-\begin{problem*}{27.64}
+\begin{problem*}{27.64} % magnetic force on charges
A particle of charge $q>0$ is moving at speed $v$ in the
$+z$-direction through a region of uniform magnetic field \vect{B}.
The magnetic force on the particle is $\vect{F}=F_0(3\ihat+4\jhat)$,
-\begin{problem*}{27.68}
+\begin{problem*}{27.68} % rail guns
A $3.00\U{N}$ metal bar, $1.50\U{m}$ long and having a resistance of
$10.0\U{\Ohm}$, rests horizontally on conducting wires connecting it
to the circuit shown in Fig.~27.62. The bar is in a uniform,
-\begin{problem*}{27.73}
+\begin{problem*}{27.73} % magnetic force on wires
A long wire carrying a $6.00\U{A}$ current reverses direction by means
of two right-angle bends, as shown in Fig.~27.64. The part of the
wire where the bend occurs is in a magnetic field of $0.666\U{T}$
\newcommand{\dB}{d\vect{B}}
\newcommand{\dl}{d\vect{l}}
-\begin{problem*}{28.12}
+\begin{problem*}{28.12} % Biot-Savart law, magnetic field from wires
Two parallel wires are $5.00\U{cm}$ apart and carry currents in
opposite directions, as shown in Fig.~28.37. Find the magnitude and
direction of the magnetic field at point $P$ due to the two
-\begin{problem*}{28.18}
+\begin{problem*}{28.18} % magnetic field from wires
Two long, straight wires, one above the other, are seperated by a
distance $2a$ and are parallel to the $x$-axis. Let the $+y$-axis be
in the plane of the wires in the direction from the lower wire to the
-\begin{problem*}{28.23}
+\begin{problem*}{28.23} % magnetic field from wires
Four long, parallel power lines each carry $100\U{A}$ currents. A
cross-sectional diagram of these lines if a square, $20.0\U{cm}$ on
each side. For each of the three cases shown in Fig.~28.41, calculate
%\newcommand{\dB}{d\vect{B}}
%\newcommand{\dl}{d\vect{l}}
-\begin{problem*}{28.30}
+\begin{problem*}{28.30} % Biot-Savart law, magnetic field from wires
Calculate the magnitude and direction of the magnetic field at point
$P$ due to the current in the semicircular section of wire shown in
Fig.~28.46. (\emph{Hint:} Does the current in the long, straight
-\begin{problem*}{28.60}
+\begin{problem*}{28.60} % magnetic field from wires
Figure~28.54 shows an end view of two long, parallel wires
perpendicular to the $xy$-plane, each carrying a current $I$ but in
opposite directions. \Part{a} Copy the diagram, and draw vectors to
-\begin{problem*}{28.62}
+\begin{problem*}{28.62} % magnetic force on wires, magnetic field from wires
A pair of long, rigid metal rods, each of length $L$, lie parallel to
each other on a perfectly smooth table. Their ends are connected by
identical, very light conducting springs of force constant $k$
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