# 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

rˆ

(c) +

σ

4πε0r

2

rˆ

(d) −

4πa2σ

4πε0r

2

rˆ

(e) +

4πa2σ

4πε0r

2

rˆ

(f) −4πa2σ + 8πb2σ

4πε0r

2

rˆ

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

rˆ

(c) +

σ

4πε0r

2

rˆ

(d) −

4πa2σ

4πε0r

2

rˆ

(e) +

4πa2σ

4πε0r

2

rˆ

(f) −4πa2σ + 8πb2σ

4πε0r

2

rˆ

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 =

2σ

ε0

xˆ, E~

III =

σ

ε0

xˆ.

(b) E~

I = −

σ

2ε0

xˆ, E~

II =

4σ

ε0

xˆ, E~

III = −

σ

ε0

xˆ.

(c) E~

I = −

σ

2ε0

xˆ, E~

II =

5σ

2ε0

xˆ, E~

III =

σ

2ε0

xˆ.

(d) E~

I = −

2σ

ε0

xˆ, E~

II =

3σ

2ε0

xˆ, E~

III =

2σ

ε0

xˆ.

(e) E~

I =

3σ

ε0

xˆ, E~

II =

σ

ε0

xˆ, E~

III =

−2σ

ε0

xˆ.

(f) E~

I =

3σ

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