ADDITIONS TO WOLFSON PROBLEMS AND PROBLEMS FROM OTHER TEXTS
JULY 22 - JULY 28
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).
33. A single-turn current loop, carrying a current of 4.00 A,
is in the shape of a right triangle with sides 50.0, 120,
and 130 cm. The loop is in a uniform magnetic field of
magnitude 75.0 mT whose direction is parallel to the
current in the 130 cm side of the loop. (a) Find the
magnitude of the magnetic force on each of the three
sides of the loop. (b) Show that the total magnetic
force on the loop is zero.
(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?
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.
WOLFSON - CHAPTER 30
8. (c) In a configuration called a "Helmholtz coil",
the two coils in Fig. 30-47 each have N turns, carry
a current I in the same direction and are separated
by a distance equal to their radius R. Find the
magnitude of the net magnetic field on the axis
midway between the two coils.
E4. This is the exercise accompanying Example 30-3 on page 780.
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.)
(P prefixes) HRW Problem Supplement #1 - CHAPTER 31
90. The figure for this problem is Fig. 31-30, except
that the magnitude of B is decreasing, rather than
increasing. A uniform magnetic field is confined to
a cylindrical volume of radius 10 cm. The magnitude
of B is decreasing at a constant rate of 10 mT/s.
What are the instantaneous accelerations (direction
and magnitude) experienced by an electron placed
(a) 5 cm below the center of the cylinder;
(b) at the center of the cylinder; and
(c) 5 cm above the center of the cylinder.
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?
27. At a certain place, Earth's magnetic field has
magnitude B = 0.590 gauss and is inclined downward at
an angle of 70.0 degrees to the horizontal. A flat
horizontal circular coil of wire with a radius of
10.0 cm has 1000 turns and a total resistance of
85.0 Ohms. It is connected to a meter with 140 Ohm
resistance. The coil is flipped through a half-
revolution about a diameter, so that it is again
horizontal. How much charge flows through the meter
during the flip? (HINT: Wolfson 31: 63 is similar.)
WOLFSON - CHAPTER 32
E5. This is the exercise accompanying Example 32-1 on page 834.