Download Homework #3 consists of only one part as follows:

Physics 122 Spring 2017 – Document #08: Homework #03
page 1 of 9
PHYS 122: Homework #03
January 31, 2017
Homework #3 consists of only one part as follows:
• There is NO Pre-lecture video and NO Online homework assignment due. These components of homework will continue after the First
Hour Exam
• Written Homework #3 is due Monday, February 6 at 5 PM to the
box outside of Rock 207.
Announcements:
• First Hour Exam (worth five percent of your grade) will be given Friday, February 10, 9:30
AM in lecture.
Assignment continues next page....
Physics 122 Spring 2017 – Document #08: Homework #03
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This Writte homework due in Box outside of Rock 207:
5:00 PM Sharp, Monday February 6, 2017
Problem 1:
Force on a charged particle due to B-field:
An experiment is conducted in a laboratory as follows: A particle with a charge +q and mass m
enters a rectangular region of space as show in the figure. Within this region there is an magnetic
~ applied into the page as shown. However B varies with time as follows:
field B
• For times t < t1 , B = 0
• For times t1 < t < t2 , B = B1
• For times t > t2 , B = 2B1
Assume that the time t1 corresponds to the position of the particle at point P as seen in this
figure. Assume that time t2 is a fairly long time after t1 . Sketch the path of this particle for all
times t > t1 directly on the figure. Assume that B1 is strong enough to keep the particle trapped
in the region. Ignore gravity.
B
+q
P
v
Physics 122 Spring 2017 – Document #08: Homework #03
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Problem 2:
Perspective View
Side View
conducting
plate
conducting
plate
conducting plate
B0
q0
q0
+
z
x
B0
d
d
VB
VB
d
d
d
d
conducting plate
z
+
conducting plate
y
x
A positively charged particle with given charge q0 and mass m0 is moving within a region of
~ = +B0 ̂ as shown. As a result of the force on the particle due to
uniform magnetic field given by B
the magnetic field, the particle moves with uniform circular motion on a circle of given diameter d
as shown. For this problem ignore gravity.
Part (a) – Is the particle traveling clockwise or counter-clockwise as show? Explain how you
know this.
Part (b) – In terms of the given parameters, what is the value of the speed of the particle as it
travels on the circular path? For this part, assume that the plates above and below are electrically
neutral. Explain your work.
Part (c) – Assume that at the instant that the particle is at the position shown in the figure
above, both switches are closed so that a battery with voltage VB is connected to the upper and
lower conducting plates as shown. What is the electric field between the plates? Be sure to give
your answer as a vector expression. Explain how you know this.
Part (d) – Assume that as a result of the application of the electric field as described in part
(c), the path of the particle is deflected so that it then hits the lower plate. Determine the speed of
the particle when it hits the lower plate in terms of the given parameters. Explain your work.
Physics 122 Spring 2017 – Document #08: Homework #03
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Problem 3:
Side View
Perspective View
Ι0
Ι0
d
+σ0
d
+σ0
d
d
P
P
d
d
−2σ0
−2σ0
z
z
y
x
x
The above plot shows an arrangement of two infinite charged plates. The upper plate has
positive surface charge density +σ0 and the lower plate has negative surface charge density −2σ0 .
The separation between the plates is 2d. Also, at a distance d above the upper plate is an infinite
wire carrying a current I0 in the x-direction as shown.
a) Consider the point P which is located half-way between the plates. What is the electric field
at point P ? Write down your answer as a vector using the coordinate system shown: x points right,
y points back (into page) and z points up. Be sure to explain how you determined your answer.
b) What is the magnetic field at point P ? Write down your answer as a vector using the
coordinate system shown. Be sure to explain your work.
c) Now particle with positive charge q0 is placed at point P and is given an initial velocity
~v = v0 ı̂. What is the value of the speed v0 that will allow the particle to move in a straight line
without being deflected in any direction? Here ignore gravity! Write your answer in terms of the
parameters given. Be sure to explain your answer.
Hint: Unless you are told otherwise, assume that a wire with a non-zero electric current
is nonetheless electrically neutral.
Physics 122 Spring 2017 – Document #08: Homework #03
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Problem 4:
Consider a set of six long straight wires arranged in a hexagon as shown. The wires run
perpendicular to the page. The current in each wire is either I2 =2.00 Amps or I3 =3.00 Amps as
indicated. The length of the each side of the hexagon is given by d=5.00 cm.
What is the magnitude and direction of the magnetic field at point P ? Note: you might want
to define a coordinate system here to indicate the direction as clearly as possible. Explain how you
determined this. Give your answer in terms of symbolic variables and then numerically with the
proper handling of units.
Note: current into the page is represented by an “X” on the wire, current out of the page
is represented by a dot.
2A
2A
P
3A
2A
3A
2A
Hint: Remember that the magnetic field is applied in the tangential direction, according to the
Right Hand Rule. So be careful with your application of symmetry here.
Physics 122 Spring 2017 – Document #08: Homework #03
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Problem 5: Lightbulb Circuit – From a past First Hour Exam
switch 2
+
−
Bulb A
Bulb C
Bulb B
switch 1
A circuit is constructed as shown above. The voltage source applies a fixed voltage Vs at the
front of the source relative to the back. Assume each bulb can be modeled as an identical resistors
of resistance R.
Part (a) – : Assume that the switches are open as shown. In terms of the parameters given calculate
the current though each of the three bulbs. Rank the bulbs in order of increasing brightness.
Explain your work.
Part (b) – : Now Suppose we close Switch 1 while leaving Switch 2 open. Now, again, calculate
the current though each of the three bulbs. Rank the bulbs in order of increasing brightness.
Explain your work.
Part (c) – : Now suppose we close Switch 2 while leaving Switch 1 also still closed. Now,
again, calculate the current though each of the three bulbs. Rank the bulbs in order of increasing
brightness. Explain your work.
Physics 122 Spring 2017 – Document #08: Homework #03
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Problem 6: Fields – From a previous First Hour Exam
solenoid
y
+λ 0
+λ 0
x
z
Iw
Iw
Rs
Is
View looking
into solenoid
is shown on
the next page.
L
Suppose you are given a configuration of charges and currents as shown above and also on the
next page:
• A large solenoid with a given constant positive current Is is constructed with a given radius
Rs and length L as shown. The total number of turns of the wire around the solenoid is given
as N . The solenoid is coaxial with the “z-axis” of our coordinate system as shown.
• Inside the solenoid we find two point charges positioned as shown (next page). Each charge
is a distance D up from the y = 0 plane and also a distance D either side of the x = 0 plane
as shown. One charge has a given value +Q0 and the other charge has a given value −3Q0 .
• Also inside the solenoid is an electrically neutral straight wire that carries a current Iw in the
positive z-direction. The wire is coaxial with the solenoid.
• Also inside the solenoid is a fixed line of charge with linear charge density λ0 . The line of
charge is parallel to the z-axis and is positioned as shown at a distance 2D above the y = 0
plane.
~ and B
~ at point P which is positioned at
Calculate the total electric and magnetic field, E
(x, y, z) = (0, D, 0) as shown on the next page. Your answer should be given as a vector expression
in terms of the given parameters. Explain your work.
Note: In this problem assume that the amount of conducting materials in the wire and solenoid
are small enough so that you can neglect any distorting effect that they might have on the electric
field at point P .
See next page for cross-sectional picture!
Physics 122 Spring 2017 – Document #08: Homework #03
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Figure For Problem 6:
View into solenoid cylinder from right side:
Note: Positive-z axis is coming out of the page!
y
solenoid
N turns
s
line
charge
+Q 0
+λ 0
P
D
Current
in each
turn =
I
D
wire
−3Q0
x
Iw
Physics 122 Spring 2017 – Document #08: Homework #03
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Problem 7: Another Circuit Problem
R
R
R
+
switch Y
A
+
V2
V2
P
+
B
V1
+
switch X
V1
ground
A circuit is constructed as shown above. There are four voltage sources as labeled each with
given voltage V1 or V2 as shown. Assume that V1 > V2 . Assume each bulb can be modeled as an
identical resistors of resistance R, same as each resistor.
Part (a): Assume that both switches are open as shown. In terms of the parameters given, calculate
the current though Bulb B. Explain your work.
Part (b): Assume that both switches are open as shown. In terms of the parameters given, calculate
the voltage relative to ground as measured at point P as shown above. Explain your work.
Part (c): Now suppose we close Switch X while leaving Switch Y open. Rank the brightness of
the two bulbs, A and B. Which of these two bulbs are brighter? Or are they the same brightness?
Explain your work.
Part (d): Now suppose we close Switch Y while also leaving closed Switch X. In terms of the
given parameters, what is the current through the topmost resistor? Explain your work.