Week 7

Discussion Problems for the week of Feb 18, 2013
Part 1 (exam 3 prep for Ch. 20 and 21)
1. A resistor is connected across the terminals of a 9.0-V battery, which delivers 1.1 × 10 5 J of
energy to the resistor in six hours. What is the resistance of the resistor?
16 Ω
2. Tungsten has a temperature coefficient of resistivity of 0.0045 (C°) -1 . A tungsten wire is
connected to a source of constant voltage via a switch. At the instant the switch is closed, the
temperature of the wire is 28 °C, and the initial power delivered to the wire is P 0 . At what wire
temperature will the power that is delivered to the wire be decreased to ½P 0 ?
250° C
3. To save on heating costs, the owner of a greenhouse keeps 660 kg of water around in barrels.
During a winter day, the water is heated by the sun to 10.0 °C. During the night the water freezes into
ice at 0.0 °C in nine hours. What is the minimum ampere rating of an electric heating system (240 V)
that would provide the same heating effect as the water does?
32 A
4. The current in the 8.00-Ω resistor in the drawing is 0.500 A. Find
the current in
(a) the 20.0-Ω resistor and in
(b) the 9.00-Ω resistor.
(a) 0.750 A
(b) 2.11 A
5. Determine the voltage across the 5.0-Ω resistor in the
drawing. Which end of the resistor is at the higher potential?
0.75 V. Left end is at higher potential.

6. Four identical capacitors are
connected with a resistor in two different
ways. When they are connected as in part a of
the drawing, the time constant to charge up
this circuit is 0.72 s. What is the time constant
when they are connected with the same
resistor, as in part b?
0.29 s
7. In the model of the hydrogen atom created by Niels Bohr, the electron moves around the
proton at a speed of 2.2 × 10 6 m/s in a circle of radius 5.3 × 10 -11 m. Considering the orbiting electron to
be a small current loop, determine the magnetic moment associated with this motion. (Hint: The
electron travels around the circle in a time equal to the period of the motion.)
9.3 × 10 -24 A · m 2
8. The magnetic field produced by the solenoid in a magnetic resonance imaging (MRI) system
designed for measurements on whole human bodies has a field strength of 7.0 T, and the current in the
solenoid is 2.0 × 10 2 A. What is the number of turns per meter of length of the solenoid? Note that the
solenoid used to produce the magnetic field in this type of system has a length that is not very long
compared to its diameter. Because of this and other design considerations, your answer will be only an
approximation.
2.8 × 10 4 turns/m
Part 2 more on Ch 21.
9. The drawing shows a thin, uniform rod that has a length of
0.45 m and a mass of 0.094 kg. This rod lies in the plane of the
paper and is attached to the floor by a hinge at point P. A uniform
magnetic field of 0.36 T is directed perpendicularly into the plane
of the paper. There is a current I = 4.1 A in the rod, which does not
rotate clockwise or counterclockwise. Find the angle θ. (Hint: The
magnetic force may be taken to act at the center of gravity.)
44°

10. The coil in the Figure contains 410 turns and has an area per turn
of 3.1 × 10 -3 m 2 . The magnetic field is 0.23 T, and the current in the coil is
0.26 A. A brake shoe is pressed perpendicularly against the shaft to keep
the coil from turning. The coefficient of static friction between the shaft
and the brake shoe is 0.76. The radius of the shaft is 0.012 m. What is the
magnitude of the minimum normal force that the brake shoe exerts on
the shaft?
8.3 N
11. A square coil of wire containing a single turn is placed in a uniform 0.25-T
magnetic field, as the drawing shows. Each side has a length of 0.32 m, and the
current in the coil is 12 A. Determine the magnitude of the magnetic force on each
of the four sides
0.96 N for the top and bottom sides, 0 for the other two.
12. T he two conducting rails in the drawing are tilted
upward so they each make an angle of 30.0° with respect to
the ground. The vertical magnetic field has a magnitude of
0.050 T. The 0.20-kg aluminum rod (length = 1.6 m)
slides without friction down the rails at a constant velocity.
How much current flows through the rod?
14 A
13. A long, cylindrical conductor is solid throughout and has a radius R. Electric charges flow
parallel to the axis of the cylinder and pass uniformly through the entire cross section. The
arrangement is, in effect, a solid tube of current I 0 . The current per unit cross-sectional area (i.e., the
current density)
is I 0 /(πR 2 ). Use Ampère's law to show that the magnetic field inside the conductor at a distance r from
the axis is μ 0 I 0 r/(2πR 2 ). (Hint: For a closed path, use a circle of radius r perpendicular to and centered on
the axis. Note that the current through any surface is the area of the surface times the current density.)
The answer is a proof.