```           ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS

JULY 19 - JULY 26

Young and Freedman - 11th Ed - CHAPTER 27
(d) For each of the above magnetic fields, what
will be the maximum kinetic energy of the loop if
it is released from rest from the position shown
in Figure 27.60 (you may consider the loop to be
pivoted about the y-axis and you may ignore all
friction)?

Young and Freedman - 11th Ed - CHAPTER 28
67.  To get credit for this problem, you must show
carefully how to use the Biot-Savart Law to arrive

Young and Freedman - 11th Ed - CHAPTER 29
(c) What is the magnitude of the induced electric
field at a point just outside the center of the
solenoid (lengthwise) and 4.00 cm from the axis of
the solenoid?  (d) Using Figure 29.46 (p. 1145),
and applying that figure to the situation of this
problem, what would be the direction of the induced
electric field in part (a) of this problem?

(b) What is the mutual inductance of this two-coil
geometry?  (Note that, in part (a), the question
is asking only for the average induced EMF in the
second winding due to the change of current in the
first winding; in other words, you are to ignore
the back EMF in the second winding due to its
self inductance.)

63.  The rod in this problem is intended to be the moving
part in a simple DC generator.  Here is a figure
of such a generator; the connecting wires are not
shown.  This problem is most straightforwardly done
by integrating vcrossBdotdl over the length of the
moving rod (note that v in this integral will not

76.  Note that the metal rails in the figure for this
problem are drawn in gray; the thin black lines
represent a non-metal frame.  For part (b), remember
that the terminal speed is the maximum speed, i.e.
the speed at which the acceleration becomes zero.

Young and Freedman - 11th Ed - CHAPTER 30
50.  The main purpose of this problem is to calculate
the inductance of a length of coaxial cable (i.e.
part (d)).  The problem assumes (but does not
state) that the cable is being used to carry high
frequency alternating currents (like a cable carrying
a TV signal); in such a case the currents would be
largely confined to the outer surface of the inner
wire and the inner surface of the outer tube (i.e.
the magnetic field is confined to the nonconducting
space between the two metal pieces).  So the flux
calculated in part (c) is in fact the total flux.
Part (b) is asking you to turn the 2D flux integral
into a 1D integral (the integral over dl being
done implicitly); you may just ignore part (b).
And in part (c), the words "over the volume" are
silly; flux is always an integral over an area, so
the integral is over a rectangular area perpendicular
to the magnetic field between the two pieces of metal.

Halliday and Resnick - 2nd Ed - CHAPTER 30
9.  A stationary circular wall clock has a face with a
radius of 15 cm.  Six turns of wire are wound around
its perimeter; the wire carries a current of 2.0 A in
the clockwise direction.  The clock is located where
there is a constant, uniform external magnetic field
of magnitude 70 mT (but the clock still keeps perfect
time).  At exactly 1:00 p.m., the hour hand of the
clock points in the direction of the external magnetic
field.  (a) After how many minutes will the minute hand
point in the direction of the torque on the winding due
to the magnetic field?  (b) Find the torque magnitude.

22.  An electric field of 1.50 kV/m and a magnetic field of
0.400 T act on a moving electron to produce no net force.
(a) Calculate the minimum speed v of the electron.
(b) Draw the vectors E, B, and v (E, B, and v are vector
symbols).

29.  An alpha particle (q = +2e, m = 4.00 u) travels in a
circular path of radius 4.50 cm in a uniform magnetic
field with B = 1.20 T.  Calculate (a) its speed, (b) its
period of revolution, (c) its kinetic energy in electron-
volts, and (d) the potential difference through which it
would have to be accelerated to achieve this energy.

31.  An electron has an initial velocity of
(12.0 km/s)j + (15.0 km/s)k and a constant acceleration
of (2.00 Tm/s^2)i in a region in which uniform electric
and magnetic fields are present.  If B = (400 microT)i,
find the electric field E (E and B are vectors).

(P prefixes) HRW Problem Supplement #1 - CHAPTER 30
73.  A long, hollow cylindrical conductor (inner radius
= 2.0 mm, outer radius = 4.0 mm) carries a current
of 24 A distributed uniformly across its cross
section.  A long thin wire that is coaxial with
the cylinder carries a current of 24 A in the
opposite direction.  What are the magnitudes of
the magnetic fields (a) 1.0 mm, (b) 3.0 mm, and
(c) 5.0 mm from the central axis of the wire and
cylinder?

WOLFSON - CHAPTER 30
42.  A conducting slab extends infinitely in the x and y
directions and has thickness h in the z direction.
It carries a uniform current density vecJ = J(veci)
(vec indicates that the first J and the i are vectors,
-- the veci is the unit vector in the x direction).
Find the magnetic field strength (a) inside and
(b) outside the slab, as functions of the distance z
from the center plane of the slab.

48.  A long solenoid with n turns per unit lengths carries
a current I.  The current returns to its driving
battery along a wire of radius R that passes through
the solenoid, along its axis.  Find expressions for
(a) the magnetic field strength at the surface of
the wire, and (b) the angle the field at the wire
surface makes with the solenoid axis.

57.  The figure below shows a wire of length L carrying
current fed by other wires that are not shown (the
current direction is to the right).  Point A lies
on the perpendicular bisector, a distance y from the
wire.  Show how to use the Biot-Savart Law to
demonstrate that the magnetic field at A due to the
straight wire alone has magnitude

(mu_0(I)L)/((2pi)y(sqrt(L^2+4y^2))).

What is the field direction?

_  . B            . A

y

-  ------------------------------  I -->

|<--           L          -->|

58.  Point B in the figure above lies a distance y
perpendicular to the end of the wire.  Show how to
use the Biot-Savart Law to demonstrate that the
magnetic field at B due to the straight wire alone
has magnitude

(mu_0(I)L)/((4pi)y(sqrt(L^2+y^2))).

What is the field direction?

68.  A solid conducting wire of radius R runs parallel
to the z axis and carries a current density given by
vecJ = J_0(1-(r/R))veck, where J_0 is a constant and
r the radial distance from the wire axis (vec
indicates that the first J and the k are vectors,
-- the veck is the unit vector in the z direction).
Find expressions for (a) the total current in the
wire, (b) the magnetic field strength for r > R,
and (c) the magnetic field strength for r < R.

FISHBANE PROBLEMS - CHAPTER 30
32.  Consider a toroidal solenoid with a square cross
section, each side of which has length 3 cm.
The inner wall of the torus forms a cylinder of
radius 12 cm.  The torus is wound evenly with
200 turns of 0.3 mm-DIAMETER copper wire.  The
wire is connected to a 3.0 V battery with
negligible internal resistance.  (a) Calculate
the largest and smallest magnetic field across
the cross section of the toroid.  (b) Calculate
the absolute value of the magnetic flux through
one turn of the toroidal solenoid.  (c) Do you
need to cool the solenoid?  (Calculate the heat
created per second when current is flowing.)

Halliday and Resnick - 2nd Ed - CHAPTER 31
5.  A square loop of wire of edge a carries a current i.
Show that the value of B at the center of the square
is given by

B =(2sqrt2)(mu_0)(i)/(pi)a

Hint: You may use the result of Wolfson 30: 57.

25.  A circular loop of radius 12 cm carries a current of
15 A.  A flat coil of radius 0.82 cm, having 50 turns
and a current of 1.3 A, is concentric with the loop.
(a) What magnetic field strength B does the loop
produce at its center?  (b) What torque acts on the
coil?  Assume that the planes of the loop and coil
are perpendicular and that the magnetic field due to
the loop is essentially uniform throughout the
volume occupied by the coil.

Halliday and Resnick - 2nd Ed - CHAPTER 32
7.  An elastic conducting material is stretched into a
circular loop of 12.0 cm radius.  It is placed with
its plane perpendicular to a uniform 0.800 T
magnetic field.  When released, the radius of the
loop starts to shrink at an instantaneous rate of
75.0 cm/s.  What EMF is induced in the loop at
that instant?

WOLFSON - CHAPTER 32
9.  A rectangular loop of length L and width w is
located a distance a from a long, straight wire.
What is the mutual inductance of this arrangement?
The picture for this problem is Y&F Figure 29.39 on
page 1143, with b-a in that figure equal to w in
this problem statement.
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