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Material Type: Quiz; Class: Essential Physics; Subject: Physics; University: Duquesne University; Term: Unknown 2000;
Typology: Quizzes
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Example 9: Chapter 21, #
Due to friction with the air, an airplane has acquired a net charge
of
€
− 5
C. The plane moves with a speed of
€
2
m/s at
an angle
€
θ with respect to the earth’s magnetic field, the
magnitude of which is
€
− 5
T. The magnetic force on the
airplane has a magnitude of
€
− 7
N. Find the angle
€
θ. (There
are two possible angles.)
Example 10: Chapter 21, #
In New England, the horizontal component of the earth’s magnetic
field has a magnitude of
€
− 5
T. An electron is shot vertically
straight up from the ground with a speed of
€
6
m/s. What is
the magnitude of the acceleration caused by the magnetic force?
Ignore the gravitational force acting on the electron.
Example 12: Chapter 21, #
A charge of - 8.3 μC is traveling at a speed of 7.4 x 10
6
m/s in a
region of space where there is a magnetic field. The angle between
the velocity of the charge and the field is 52˚. A force of magnitude
5.4 x 10
N acts on the charge. What is the magnitude of the
magnetic field?
Chapter 21.3 Motion of Charged Particles in Magnetic Fields
From the previous section, if there is a charged particle moving
perpendicular to a magnetic field, that particle will feel a force.
How does this force affect its motion?
Thus if the entire velocity of the charged particle is perpendicular
to the magnetic field, the motion of the particle is circular. Now,
back when we were talking about acceleration, I mentioned there
were three different ways an object can accelerate (because
acceleration is a vector)…
the object’s speed can change (the magnitude changes)
the object’s direction can change (with the speed staying
constant)
class)
Chapter 21. 4 The Mass Spectrometer
Using Newton’s Second Law for charged particles moving in a
magnetic field (and ignoring other forces except for the magnetic
force) you find that the radius of the circular path depends on the
mass of the particle.
€
F = m
a ∑
€
B
= q
v sin θ Let
€
θ = 90˚
This behavior is extremely useful. Machines called mass
spectrometers exploit this behavior for different purposes.
As the book points out, physicists use mass spectrometers to
determine the relative abundances of isotopes (as well as their
masses). Chemists use these to help them identify unknown
molecules, and anesthesiologists use them to gather information on
the gases in a patient’s lungs.
Example 13:
An electron moves at a speed of
€
6
m/s perpendicular to a
constant magnetic field. The path is a circle of radius
€
− 3
m.
(a) Draw a sketch showing the magnetic field and electron’s path.
(b) What is the magnitude of the field? (c) Find the magnitude of
the electron’s acceleration.
Example 15: Chapter 21, #
Two isotopes of carbon, carbon-12 and carbon-13, have masses of
€
− 27
kg and
€
− 27
kg, respectively. These two
isotopes are singly ionized (+ e ) and each is given a speed of
€
5
m/s. The ions then enter the bending region of a mass
spectrometer where the magnetic field is 0.8500 T. Determine the
spatial separation between the two isotopes after they have traveled
through a half-circle.
Example 16: Chapter 21, #
A beam of protons moves in a circle of radius 0.23 m. The protons
move perpendicular to a 0.25-T magnetic field. (a) What is the
speed of each proton? (b) Determine the magnitude of the
centripetal force that acts on each proton.
Example 18: Chapter 21, #
A particle of mass 6.8 x 10
kg and charge +7.2 μC is traveling
due east. It enters perpendicularly a magnetic field whose
magnitude is 3.0 T. After entering the field, the particle completes
one-half of a circle and exits the field traveling due west. How
much time does the particle spend in the magnetic field?
