Problem Set 4
Due: see website for due date
Chapter 21: Magnetic Fields and Forces
Questions: 3, 6, 12, 16
Problems: 6, 11, 14, 18, 23, 34, 37, 59
Q21.3: The drawing shows four situations in which a positively charged particle is
moving with a velocity v through a magnetic field B. In each case, the magnetic field is
directed out of the page toward you, and
the velocity is directed to the right. In only
one of these drawings is the magnetic force
F physically reasonable.
Which drawing is it? (a) 1; (b) 2; (c) 3; (d) 4.
Q21.6: Three particles are moving perpendicular to a uniform magnetic field and travel
on circular paths (see the drawing). The particles have
the same mass and speed. List the particles in order of
their charge magnitude, largest to smallest.
(a) 3, 2, 1; (b) 3, 1, 2; (c) 2, 3, 1; (d) 1, 3, 2; (e) 1, 2, 3.
Q21.12: Four views of a horseshoe magnet and a current-carrying wire are shown in the
drawing. The wire is perpendicular to the page,
and the current is directed out of the page toward
you. In which one or more of these situations
does the magnetic force on the current point due
north?
(a) 1 and 2; (b) 3 and 4; (c) 2; (d) 3; (e) 1.
Q21.16: The drawing shows four situations in which two very long wires are carrying the
same current, although the
directions of the currents may be
different. The point P in the
drawings is equidistant from
each wire. Which one (or more)
of these situations gives rise to a
zero net magnetic field at P? (a) 2 and 4; (b) Only 1; (c) Only 2; (d) 2 and 3; (e) 3 and 4.
P21.6: A particle that has an 8.2 μC charge moves with a velocity of magnitude 5.0×105
m/s along the +x axis. It experiences no magnetic force, although there is a magnetic
field present. The maximum possible magnetic force that the charge could experience
has a magnitude of 0.48 N. Find the magnitude and direction of the magnetic field. Note
that there are two possible answers for the direction of the field.
Answer: 0.12 T, ±x
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P21.11: The electrons in the beam of a television tube have a kinetic energy of 2.40×10-15
J. Initially, the electrons move horizontally from west to east. The vertical component of the
earth’s magnetic field points down, toward the surface of the earth, and has a magnitude
of 2.00×10-5 T. (a) In what direction are the electrons deflected by this field component?
(b) What is the acceleration of an electron in part (a)?
Answer: South, 2.55×1014 m/s2
P21.14: A charged particle with a charge-to-mass ratio of q/m = 5.7×108 C/kg travels on
a circular path that is perpendicular to a magnetic field whose magnitude is 0.72 T. How
much time does it take for the particle to complete one revolution?
Answer: 1.5×10-8 s
P21.18: Suppose that an ion source in a mass spectrometer produces doubly ionized
gold ions (Au2+), each with a mass of 3.27×10-25 kg. The ions are accelerated from rest
through a potential difference of 1.00 kV. Then, a 0.500-T magnetic field causes the ions
to follow a circular path. Determine the radius of the path.
Answer: 0.0904 m
P21.23: A proton with a speed of 3.5×106 m/s is shot into a region between
two plates that are separated by a distance of 0.23 m. As the drawing
shows, a magnetic field exists between the plates, and it is perpendicular to
the velocity of the proton. What must be the magnitude of the magnetic field
so the proton just misses colliding with the opposite plate?
Answer: 0.16 T
P21.34: The drawing shows a wire composed of three segments, AB, BC,
and CD. There is a current of I = 2.8A in the wire. There is also a magnetic
field B (magnitude = 0.26 T) that is the same everywhere and points in the
direction of the +z axis. The lengths of the wire segments are LAB = 1.1 m,
LBC = 0.55 m, and LCD = 0.55 m. Find the magnitude of the force that acts on
each segment.
Answer: (0.80, 0.40, 0) N
P21.37: A loop of wire has the shape of a right triangle (see the drawing) and
carries a current of I = 4.70 A. A uniform magnetic field is directed parallel to
side AB and has a magnitude of 1.80 T. (a) Find the magnitude and direction of
the magnetic force exerted on each side of the triangle. (b) Determine the
magnitude of the net force exerted on the triangle.
Answer: (0, 24.2, 24.2) N; (0, out of the page, into the page)
P21.59: Two long, straight wires are separated by 0.120 m. The wires carry currents of
8.0 A in opposite directions, as the drawing indicates. Find the magnitude of the net
magnetic field at the points labeled (a) A and (b) B.
Answer: 4.3×10-5 T, 5.3×10-5 T
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