Physics: Electromagnetism
Spring 2007
Physics: Electricity and Magnetism
Spring 2007
PROBLEM SET 8
Issued: Friday, March 30, 2007
Due: Thursday, April 5, 2007, in class
“I have no special talents. I am only passionately curious.”
- Albert Einstein
http://www.deathboy.com/acme/welcome.html
Important Concepts:
(a)
(b)
(c)
(d)
The Magnetism
The Magnetic Force on a Moving Charge
The Motion of Charged Particles in Magnetic Fields
The Magnetic Force on a Current
Useful Tips:
(a) Read your textbook and class notes.
(b) Make sure you understand in-class and textbook examples. After looking at the solution presented
to you, close your notes and/or textbook and try to solve the problems on your own -- this is
crucial!
(c) When solving a problem, think whether your steps are reasonable. When answer is obtained,
think whether it makes sense; if not, explain why not and go back to find your errors in reasoning
or/and algebra. A good check is always unit analysis! Good luck!
Textbook Reading:
(a) Chapter 29 of Wolfson and Pasachoff
(b) http://www.falstad.com/vector3dm/
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Physics: Electromagnetism
Spring 2007
Problems and Exercises:
1. Some Physics Braintwisters:
a) Assume you have two steel bars. The only difference between these two bars is that one is a
permanent magnet and the other is unmagnetized. Without using any equipment, how can you tell
which one is which?
b) Magnets have two magnetic poles. If someone could build a magnet with jut one pole, a great feat
would be accomplished. Here’s one modest proposal. One could cut a steel sphere into irregular
sections, each shaped as a cone, with its sharp end pointing toward the center of the sphere.
Magnetize all the sharp ends as south poles and all the other ends as north poles. Put the magnetized
section all back together again so they form a sphere. Will the magnetized sphere have a north pole
on the outside and the south pole on inside? Will the south pole disappear, thereby creating a north
pole monopole? Please, discuss this thought experiment.
c) We know that magnetic fields never do any work on charged particles. Yet, a current-carrying wire
placed in a magnetic field will gain kinetic energy as the wire accelerates in response to the magnetic
force. How can that be? (HINT: You may find the following sources helpful in answering these
questions:
• Coombes, C. A., “Work Done on Charged Particles in Magnetic Fields.” American Journal of
Physics, 47, p 915-917 (1979).
• Mosca, E. P. “Magnetic Forces Doing Work?” American Journal of Physics 42, p 295-297
(1974). )
2. Wolfson and Pasachoff, Ch. 29, Problem 31, p. 766
3.
Wolfson and Pasachoff, Ch. 29, Problem 36, p. 766
4. Wolfson and Pasachoff, Ch. 29, Problem 38, p. 766
5.
Wolfson and Pasachoff, Ch. 29, Problem 40, p. 766
6.
Wolfson and Pasachoff, Ch. 29, Problem 41, p. 767
7.
Please, answer each question in detail:
a) If an electron in a cathode-ray tube is traveling in a straight line, what can you say about the
presence or absence of a magnetic field?
b) You have a fixed length of wire and want to use it to make a magnetic dipole with the largest
possible magnetic dipole moment. Into what shape should you wind it? Are you better off
making a single loop or N loops?
c) Can a magnetic field be used to speed up a charged particle?
d) How does the radius of the path of a charged particle in a magnetic field depends on its kinetic
energy?
8. The Figure below is a schematic diagram of a cyclotron. A charged particle starts out at the central
point and, for a given magnetic field perpendicular to the plane of motion, follows a circular path. The
cyclotron takes advantage of the fact that the time for the particle to execute a half-circle is
independent of the particle’s velocity. An alternating voltage is applied across the gap between the
two “dees” (the semicircular regions), so that, when the particle crosses the gap, the voltage acts to
accelerate it. When the particle gets to the gap again after having completed a half-circle, the voltage
has changed sign, and the particle is once again accelerated. The frequency of the oscillating voltage
must match the cyclotron frequency. In this way, the particle is always accelerated, completing ever
bigger circles in the same time, until the beam is extracted at the maximum radius.
a) If the magnetic field has strength of 1 Tesla and the circulating particle is a proton, q = + e and m
= 1.7 x 10-27 kg, what is the cyclotron frequency?
b) What is the maximum velocity of the proton for a maximum radius of 50 cm?
c) What is the corresponding maximum kinetic energy?
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Physics: Electromagnetism
Spring 2007
d) If the maximum voltage across the gap is 50 kV, how many full circles does the proton make
before it reaches its maximum energy?
e) How much time does the proton spend in the accelerator?
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