A potential difference V exists between two parallel plates that are separated by a distance d. A particle of mass m and charge +q is accelerated from rest through the potential difference, and as a result moves between the plates in a straight line in the plane of the page, as shown above. The particle reaches the right-hand plate with a speed v, passes through a hole in the plate, and enters a region containing a uniform magnetic field. The particle then follows the semicircular path shown. Gravitational effects are negligible. (a) Would the speed v of the particle be greater, smaller, or the same if the magnitude of the potential difference was greater? Explain your answer. Hole +q 01117 m Plates Region of Magnetic Field (b) A student derives the equation v = 2 for the speed of the particle. Whether or not the equation md is correct, is it consistent with your answer to part (a)? Explain your reasoning. (c) A student equates the following two expressions to determine how an increase in the magnitude of the particle's charge affects the radius of its path in the field. mv/r for the magnitude of the net force on an object in uniform circular motion with radius r qvB for the magnitude of the force on a charged particle in a magnetic field of magnitude B Describe the relationship between the particle's charge and the radius of its path indicated by these expressions, and indicate how an increase in charge affects the radius.
A potential difference V exists between two parallel plates that are separated by a distance d. A particle of mass m and charge +q is accelerated from rest through the potential difference, and as a result moves between the plates in a straight line in the plane of the page, as shown above. The particle reaches the right-hand plate with a speed v, passes through a hole in the plate, and enters a region containing a uniform magnetic field. The particle then follows the semicircular path shown. Gravitational effects are negligible. (a) Would the speed v of the particle be greater, smaller, or the same if the magnitude of the potential difference was greater? Explain your answer. Hole +q 01117 m Plates Region of Magnetic Field (b) A student derives the equation v = 2 for the speed of the particle. Whether or not the equation md is correct, is it consistent with your answer to part (a)? Explain your reasoning. (c) A student equates the following two expressions to determine how an increase in the magnitude of the particle's charge affects the radius of its path in the field. mv/r for the magnitude of the net force on an object in uniform circular motion with radius r qvB for the magnitude of the force on a charged particle in a magnetic field of magnitude B Describe the relationship between the particle's charge and the radius of its path indicated by these expressions, and indicate how an increase in charge affects the radius.
Chapter5: Electric Charges And Fields
Section: Chapter Questions
Problem 120AP: A particle of charge q and mass m is placed at the center of a uniformly charged ring of total...
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Transcribed Image Text:A potential difference V exists between two parallel plates that are
separated by a distance d. A particle of mass m and charge +q is
accelerated from rest through the potential difference, and as a result
moves between the plates in a straight line in the plane of the page, as
shown above. The particle reaches the right-hand plate with a speed v,
passes through a hole in the plate, and enters a region containing a uniform
magnetic field. The particle then follows the semicircular path shown.
Gravitational effects are negligible.
(a) Would the speed v of the particle be greater, smaller, or the same if the
magnitude of the potential difference was greater? Explain your answer.
+q
m
2qV
-
md
(b) A student derives the equation v
is correct, is it consistent with your answer to part (a)? Explain your reasoning.
Hole
Plates
Region of
Magnetic
Field
for the speed of the particle. Whether or not the equation
(c) A student equates the following two expressions to determine how an increase in the magnitude
of the particle's charge affects the radius of its path in the field.
mv²/r for the magnitude of the net force on an object in uniform circular motion with radius r
qvB for the magnitude of the force on a charged particle in a magnetic field of magnitude B
Describe the relationship between the particle's charge and the radius of its path indicated by these
expressions, and indicate how an increase in charge affects the radius.
Transcribed Image Text:(d) For the values m = 5.04 x 10-27 kg, q = 3.20 x 10-1⁹ C, v = 2.20 x 106 m/s, and B = 0.30 T, compute
the radius of the particle's circular motion.
2Vm
(e) Another student writes the equation r = √
for the radius of the path. Whether or not the
(B²+qV)
equation is correct, is it consistent with your answers to part (c) and (d)? Explain your reasoning.
(f) If the particle had a charge of -q, would its motion be the same? Justify your answer.
-d
The region of the magnetic field is replaced +V
by a wire that is in the page and has a
current directed toward the right. The
positively charged particle still moves in a
straight line between the plates.
(g) With respect to the coordinate axes
shown, in what direction is the acceleration
of the particle at the instant it passes
through the hole? Explain your reasoning.
+q
m
Hole
Plates
Wire
+y
+Z
+X
(out of page)
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