Physics 2212 GHJ

Physics 2212 GHJ
Fall 2013
Test 1
1)
Test form 901
Name ___________________________
Recitation Section (see back of test):__________
Print your name, test form number (above), and nine-digit student number in the section of the answer
card labeled "STUDENT IDENTIFICATION".
2) Bubble your test form number (ABOVE) in columns 1-3, skip column 4, then bubble in your student
number in columns 5-13.
A
3) For each free-response question, show all relevant work supporting your answer. Clearly box or underline your final
answer. “Correct” answers which are not supported by adequate calculations and/or reasoning will be counted wrong.
4) For each multiple-choice question, select the answer most nearly correct, circle this answer on your test, and bubble it in on
your answer card. Show all relevant work on your quiz.
5) Be prepared to present your Buzzcard as you turn in your test. Scores will be posted to WebAssign after they have been been
graded. Quiz grades become final when the next quiz is given.
6) You may use a simple scientific calculator capable of logarithms, exponentials, and trigonometric functions. Programmable
engineering calculators with text or graphical capabilities are not allowed. Wireless devices are prohibited.
Numerical Constants:
k = 8.99×109 N·m2/C2
e = 1.60×10–19 C
me = 9.11×10–31 kg
εo = 8.85×10–12 C2/N·m2
g = 9.81 m/s2
mp = 1.67×10–27 kg
Your test form is: 901
page 1 of 8
901
The following problem will be hand-graded. Show all your work for this problem. Make no marks and leave no space on your
answer card for it.
[I]
Three charges are arranged at the corners of a rectangle, as shown.
(A)
(12 points) What is the magnitude of the force on the lower-left
charge? Express your answer in terms of the parameters k, Q, and L.
(B)
(8 points) What is the direction of the electric field due to the top two charges, at the location of the lower-left charge?
Express your answer as an angle to three-digit precision, measured from one of the cartesian axes. Be clear about which
axis you are using (+/– x, or +/–y), and which direction (clockwise or counterclockwise) you are measuring from that axis!
Page 2 of 8
901
The following problem will be hand-graded. Show all your work for this problem. Make no marks and leave no space on your
answer card for it.
[II]
A charged metal plate has a surface density η = –24.0 nC/m2. A proton
is fired away from the plate with a speed vo = 125,000 m/s directed at
an angle θ = 36.9° from the normal.
(A)
(12 points) What maximum distance D does the proton travel away
from the plate, before turning back? Solve the problem symbolically,
making numerical substitutions only at the very end.
(B)
(8 points) When the proton finally returns to strike the plate, how far is it from its launch point? Express your answer as
a numerical multiple of D, the maximum distance found in part A.
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901
The following problem will be hand-graded. Show all your work for this problem. Make no marks and leave no space on your
answer card for it.
[III] An insulating rod lies along the x-axis, extending from x = 0 to x = +L. A charge +Q is distributed uniformly along the rod.
(A)
(12 points) Using integration techniques, determine the magnitude and direction of the electric field at point P in the
figure, located at position xp = –L. Express your answer symbolically in terms of k, Q, and L, along with a Cartesian unit
vector for direction.
[Hint: for a tiny subsegement δx of the rod at position x, what is its distance from point P, and what charge δq does it have?]
(B)
(8 points) A naïve student attepts to approximate the charged rod as if it were a single point charge located at the
midpoint of the rod, xm = +L/2. Compute the percent error that the student obtains (in comparison to your exact answer
in Part A), if this crude approximation is used. Express your answer as a numerical percentage, not an algebraic
expression. [Recall that %error is calculated as (approx – exact) / exact.]
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901
(1)
(2)
Question value 8 points
A point charge –Q is fixed at the origin. A small electric dipole (size s, charges ±q) is placed on the
positive y-axis as shown at right. When the dipole is released, what interaction(s) will it experience?
(a)
It will experience a torque directed into the page, followed by
a force directed straight down.
(b)
It will experience a torque directed to the right.
(c)
It will experience a force directed to the left.
(d)
It will experience a torque directed out of the page, followed by
a force directed straight down.
(e)
It will experience a torque directed to the left, followed by
a force directed to the right.
Question value 8 points
Two identical conducting spheres A and B are in direct contact. They are initially
uncharged. A pith ball hangs from an insulating thread near A. A charged rod C
is then held near B. When this occurs, the pith ball is attracted to A, briefly
contacts the sphere, and is then repelled from A. While rod C is still held nearby,
spheres A and B are separated.
A
pith
ball
B
C
Which of the following statements best describes the resulting interactions that would be observed?
(a)
(b)
(c)
(d)
(e)
Sphere A will be repelled by all other objects.
The pith ball will be repelled by A & B, but attracted to C.
Sphere B will be attracted to all the other objects.
The pith ball will be repelled by A, but attracted to B & C.
Rod C will be attracted to all other objects.
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901
(3)
Question value 8 points
An insulating rod of length L is bent into a quarter-circle, as shown at right.
A non-uniform linrear charge distribution is then placed on the rod, given by:
𝜆 𝜃 = 𝐶 sin 𝜃 for 0 ≤ θ ≤ π/2,
where C is a positive constant. What is the total charge Q on the rod?
(4)
(a)
𝐶𝜋 2𝐿
(b)
2𝐶𝐿 𝜋
(c)
𝐶𝐿
(d)
2𝐶 𝜋
(e)
2𝐶 cos 𝜃 𝜋
Question value 8 points
A charge +2Q is placed at the origin, and a charge –Q is placed at x = +d. Where,
if anywhere, would you find a location having a net field that was exactly zero?
(a)
On the negative x-axis, at some x < –d.
(b)
On the positive x-axis, at some x > +d.
(c)
There is no place, even off at infinity, where the field is exactly zero.
(d)
On the negative x-axis, between x = 0 and x = –d.
(e)
On the positive x-axis, between x = 0 and x = +d.
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901
The next two questions involve the following situation:
A parallel-plate capacitor is formed by two square conducting sheets of length L on a side, separated by a distance d. The
plates are given charge ±Q, resulting in a field of magnitude Eo between the plates.
(5)
(6)
Question value 4 points
If the amount of charge on the plates is increased by 50%, what will be the new field strength between the plates?
(a)
Ef = (3/2) Eo
(b)
Ef = (2/3) Eo
(c)
Ef = (9/4) Eo
(d)
Ef = (1/2) Eo
(e)
Ef = 2 Eo
Question value 4 points
If the separation between the plates is decreased by 50%, what will be the new field strength between the plates?
(a)
Ef = (2/3) Eo
(b)
Ef = (1/2) Eo
(c)
Ef = (3/2) Eo
(d)
Ef = Eo
(e)
Ef = 2 Eo
Page 7 of 8
PHYS 2212 GHJ Recitation TA and Room Assignments
Tests will be returned in recitation, in the week after the test. In order to ensure that you receive your test
back as soon as possible, please enter your recitation section from the table above (G01–G07, H01–H08, or
J01-J08) on the front of this test.
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