o/Magnetic forces cause a
beam of electrons to move in a
circle.
p/You can’t isolate the poles of a
magnet by breaking it in half.
q/A magnetic dipole is made
out of other dipoles, not out of
monopoles.
was flipped when it was stuck onto the battery. By the right-hand
rule (figure d on page 677), the field must be toward the battery.
Nervous-system effects during an MRI scan example 3
During an MRI scan of the head, the patient’s nervous system
is exposed to intense magnetic fields, and there are ions moving
around in the nerves. The resulting forces on the ions can cause
symptoms such as vertigo.
A circular orbit example 4
The magnetic force is always perpendicular to the motion of the
particle, so it can never do any work, and a charged particle mov-
ing through a magnetic field does not experience any change in
its kinetic energy: its velocity vector can change its direction, but
not its magnitude. If the velocity vector is initially perpendicular
to the field, then the curve of its motion will remain in the plane
perpendicular to the field, so the magnitude of the magnetic force
on it will stay the same. When an object experiences a force with
constant magnitude, which is always perpendicular to the direc-
tion of its motion, the result is that it travels in a circle.
Figure o shows a beam of electrons in a spherical vacuum tube.
In the top photo, the beam is emitted near the right side of the
tube, and travels straight up. In the bottom photo, a magnetic field
has been imposed by an electromagnet surrounding the vacuum
tube; the ammeter on the right shows that the current through the
electromagnet is now nonzero. We observe that the beam is bent
into a circle.
self-check A
Infer the direction of the magnetic field. Don’t forget that the beam is
made of electrons, which are negatively charged! .Answer, p. 1060
Homework problem 12 is a quantitative analysis of circular orbits.
A velocity filter example 5
Suppose you see the electron beam in figure o, and you want to
determine how fast the electrons are going. You certainly can’t
do it with a stopwatch! Physicists may also encounter situations
where they have a beam of unknown charged particles, and they
don’t even know their charges. This happened, for instance, when
alpha and beta radiation were discovered. One solution to this
problem relies on the fact that the force experienced by a charged
particle in an electric field,FE=qE, is independent of its veloc-
ity, but the force due to a magnetic field,FB=qv×B, isn’t. One
can send a beam of charged particles through a space containing
both an electric and a magnetic field, setting up the fields so that
the two forces will cancel out perfectly for a certain velocity. Note
that since both forces are proportional to the charge of the parti-
cles, the cancellation is independent of charge. Such avelocity
filtercan be used either to determine the velocity of an unknown682 Chapter 11 Electromagnetism