# Field Maps and Gauss Law Homework 3 Lab Report

Name: Lab Day/Time:
Homework 3 Field Maps and Gauss’ Law
Homework is due at the beginning of the Wednesday lecture. It must be handwritten, not typeset. The multiplechoice answers must be circled. In the space after the problem, a short justification of each multiple-choice the
answer must be included. The open-response answers must be worked out clearly using good physics presentation
and will be graded on correctness and how carefully the work is explained. The problems should be worked in
the space after the problem on the assignment printout; additional paper may be used if needed. No credit will
be given for answers without appropriate supporting work. Minimum good presentation requires the following:
(1) Symbolic expression for any formula, (2) Manipulation of symbolic expressions, not numeric expressions, (3)
Substitution of numbers with units, (4) Reporting final answers with correct units and vector expressions, (5)
Enough English description to allow the reader to have some idea what you are doing without looking at the
math.
Multiple Choice Problems
The questions in this section are to be answered by circling the correct multiple-choice answer AND
providing a short justification of your answer in the space after the problem..
Homework Problem 3.1 The figure to the right shows two
charged spherical shells. The inner shell has radius a and charge
density σa = +σ. The outer shell has radius b and charge density
σb = −4σ. Calculate the electric field in Region II between the
two shells (a < r < b).
Select One of the Following:
(a) 0
(b) −
σ
4πε0r
2

(c) +
σ
4πε0r
2

(d) −
4πa2σ
4πε0r
2

(e) +
4πa2σ
4πε0r
2

(f) −4πa2σ + 8πb2σ
4πε0r
2

a
x
y
b
Air
Air
Air
I
II
III
1
Homework Problem 3.2 Two infinite parallel planes of charge
with uniform surface charge densities are parallel to the y−z plane
and equally spaced about the origin. The planes pass through
the points ±1cm. The plane passing through +1cmˆx has surface
charge density 3
4
σ. The plane passing through −1cmˆx has surface
charge density −
1
4
σ. The planes are drawn to the right. Compute
the electric field at the origin.
Select One of the Following:
(a) +σ/2ǫ0xˆ
(b) −σ/2ǫ0xˆ
(c) +σ/ǫ0xˆ
(d) −σ/ǫ0xˆ
(e) +σ/4ǫ0xˆ
x
y
3
4
1 σ
4
_ σ +
Homework Problem 3.3 The two infinite parallel planes to the
right have equal but opposite uniform charge densities, ±σ. A
particle with charge +q is placed between the planes. Rank the
magnitude of the total electric field due to the two planes and
the point charge at the four points labeled (a) through (d). The
points are equidistant from the +q particle.
Select One of the Following:
(a) Ea < Eb = Ed < Ec
(b) Ea > Eb = Ec > Ed
(c) Ea < Eb < Ec < Ed
(d) Eb = Ed < Ea < Ec
(e) Ea = Eb = Ec = Ed
+σ −σ
+q
a
b
c
d
2
Homework Problem 3.4 A point charge with charge 3nC is at +4cmˆy. Calculate the acceleration (as a vector)
of a point charge with charge −2nC and mass 1g = 1 × 10−3kg placed at point P at ~rP = −3cmˆx − 2cmˆy.
Select One of the Following:
(a) ~a = −5.36 × 10−2 m
s
2 ˆx + 1.07 × 10−2 m
s
2 ˆy
(b) ~a = +7.36 × 10−3 m
s
2 ˆx + 3.07 × 10−2 m
s
2 ˆy
(c) ~a = −3.26 × 10−3 m
s
2 ˆx + −1.07 × 10−3 m
s
2 ˆy
(d) ~a = +1.11 × 10−1 m
s
2 ˆx + 2.07 × 10−4 m
s
2 ˆy
(e) ~a = +5.36 × 10−3 m
s
2 ˆx + 1.07 × 10−2 m
s
2 ˆy
Homework Problem 3.5 If a long, thin, straight isolated wire has a linear charge density of 3.4 × 10−5C/m,
calculate the magnitude of the electric field at a point a distance 5.0m from the axis of the wire, modeling the
wire as an infinite linear charge.
Select One of the Following:
(a) 1.2 × 105 N
C
(b) 4.1 × 105 N
C
(c) 6.1 × 106 N
C
(d) 1.2 × 107 N
C
(e) 6.1 × 107 N
C
Homework Problem 3.6 A hula hoop of radius 1.0m is in a uniform electric field with magnitude 1.0 × 102 N
C
.
Its normal is parallel to the field (careful here). What is the flux through the hoop?
Select One of the Following:
(a) 310 N
Cm2
(b) 620 N
Cm2
(c) 1.0 × 102 N
Cm2
(d) 0
3
Homework Problem 3.7 If a metal sphere of radius 1cm is charged with a “D” cell battery, a charge of
1.7 × 10−12C is developed. If this sphere is then placed in a cubic box with edges of length 30.0cm. What is the
electric flux out of the box?
Select One of the Following:
(a) 2.7 × 10−15Nm2/C
(b) 4.6 × 10−14Nm2/C
(c) 1.7 × 10−4Nm2/C
(d) 5.2 × 10−3Nm2/C
(e) 0.19Nm2/C
Homework Problem 3.8 The figure to the right shows two
charged spherical shells. The inner shell has radius a and charge
density σa = −σ. The outer shell has radius b and charge density
σb = +2σ. Calculate electric field at points in Region I inside
the inner shell, at a radius of r < a.
Select One of the Following:
(a) 0
(b) −
σ
4πε0r
2

(c) +
σ
4πε0r
2

(d) −
4πa2σ
4πε0r
2

(e) +
4πa2σ
4πε0r
2

(f) −4πa2σ + 8πb2σ
4πε0r
2

a
x
y
b
Air
Air
Air
I
II
III
4
Homework Problem 3.9 Two infinite planes of charge are shown
to the right. They have charge densities 3σ and −2σ as shown.
Calculate the electric field everywhere. I II III
+3σ − 2σ x
Select One of the Following:
(a) E~
I = −
σ
ε0
xˆ, E~
II =

ε0
xˆ, E~
III =
σ
ε0
xˆ.
(b) E~
I = −
σ
2ε0
xˆ, E~
II =

ε0
xˆ, E~
III = −
σ
ε0
xˆ.
(c) E~
I = −
σ
2ε0
xˆ, E~
II =

2ε0
xˆ, E~
III =
σ
2ε0
xˆ.
(d) E~
I = −

ε0
xˆ, E~
II =

2ε0
xˆ, E~
III =

ε0
xˆ.
(e) E~
I =

ε0
xˆ, E~
II =
σ
ε0
xˆ, E~
III =
−2σ
ε0
xˆ.
(f) E~
I =

2ε0
xˆ, E~
II = 0, E~
III =
−σ
ε0
xˆ.
(g) E~
I =
σ
2ε0
xˆ, E~
II =
−5σ
2ε0
xˆ, E~
III =
−σ
ε0
xˆ.
5
Homework Problem 3.10 Consider the points A and B in the
electric field map at the right. Compare the magnitude of the
electric force exerted on a point charge with charge +q placed
at points A and B. The field is of constant magnitue into and
out-of the page.
A B
Select One of the Following:
(a) The forces are equal at A and B.
(b) The force at A is about twice as strong as the force at B.
(c) The force at A is about half as strong as the force at B.
(d) The force at A is about four times as strong as the force at B.
(e) The force at A is about one quarter as strong as the force at B.
6
Open Response Questions
Homework Problem 3.11 Three planes with charges σ,−2σ, and −σ are spaced equally along the x-axis.
Compute and draw the electric field everywhere.
7
Homework Problem 3.12 A uniform spherical volume of charge
has total charge Q = 0.200µC and radius a = 4.00cm centered
at the origin. Calculate the volume charge density, ρ. Calculate
the symbolic form of the electric field everywhere. Calculate the
electric field numerically, as a vector, at ~rP = (1.00cm, 3.00cm,
2.00cm).
air
I
II
a
x
y
8