Ch 18 Electric Fields

Chapter 18
Electric Forces &
Electric Fields

AP Learning Objectives
ELECTRICITY AND MAGNETISM
 Electrostatics
• Charge and Coulomb’s Law
• Students should understand the concept of electric
charge, so they can:
• Describe the types of charge and the attraction and
repulsion of charges.
• Describe polarization and induced charges.
• Students should understand Coulomb’s Law and the
principle of superposition, so they can:
• Calculate the magnitude and direction of the force on
a positive or negative charge due to other specified
point charges.
• Analyze the motion of a particle of specified charge
and mass under the influence of an electrostatic force.

AP Learning Objectives
ELECTRICITY AND MAGNETISM
 Electric field and electric potential (including point charges)
• Students should understand the concept of electric field, so they
can:
• Define it in terms of the force on a test charge.
• Describe and calculate the electric field of a single point
charge.
• Calculate the magnitude and direction of the electric field
produced by two or more point charges.
• Calculate the magnitude and direction of the force on a
positive or negative charge placed in a specified field.
• Interpret an electric field diagram.
• Analyze the motion of a particle of specified charge and
mass in a uniform electric field.

Table of Contents
1. The Origin of Electricity
2. Charged Objects and the Electric Force
3. Conductors & Insulators
4. Charging by Contact and by Induction
5. Coulomb’s Law
6. The Electric Field
7. Electric Field Lines
8. The Electric Field Inside a Conductor: Shielding
9. Gauss’ Law (Not AP B)
10. Copiers & Computer Printers (AP?)

Ch 18: Electric Fields
Section 1
The Origin of Electricity

The electrical nature of matter is inherent
in atomic structure.
kg10673.1 27−
×=pm
kg10675.1 27−
×=nm
kg1011.9 31−
×=em
C1060.1 19−
×=e
coulombs

 In nature, atoms are normally
found with equal numbers of
protons and electrons, so they are
electrically neutral.
 By adding or removing electrons
from matter it will acquire a net
electric charge with magnitude
equal to e times the number of
electrons added or removed, N.
Neq =

Example 1 A Lot of Electrons
How many electrons are there in one coulomb of negative charge?
Neq =
e
q
N =
C101.60
C00.1
19-
×
= 18
1025.6 ×=

18.1.1. A brass key has a net positive charge of +1.92 × 10−16
C.
Approximately, how many electrons must be added to the key to
make it electrically neutral?
a) 770
b) 960
c) 1200
d) 1800
e) 2100

18.1.2. Can an object carry a charge of 2.4 × 10−19
C?
a) Yes, if the object is a conductor.
b) Yes, if the object has electrons or protons.
c) Yes, if the object is an insulator.
d) No, because objects do not have charge.
e) No, because charge is quantized.

18.1.3. The smallest charge on a single particle has been measured
to be 1.60 × 10−19
C. What can we conclude from the fact that no
smaller charges have been measured?
a) Charge is quantized.
b) Electrons are conserved.
c) Charge is conserved.
d) Electrons have the smallest unit of charge.
e) Charge is the same as mass.

Section 2:
Charged Objects and
The Electric Force

Charged Objects
 It is possible to transfer electric charge from one object to
another?
 The body that loses electrons has an excess of positive
charge, while the body that gains electrons has an excess of
negative charge.

Law of Conservation of Electric Charge
 During any process, the net electric charge of an isolated
system remains constant (is conserved).

The Electric Force
 Like charges repel
 Unlike charges attract each other.

18.2.1. Complete the following statement: When a glass rod is
rubbed with silk cloth, the rod becomes positively charged as
a) negative charges are transferred from the rod to the silk.
b) negative charges are transferred from the silk to the rod.
c) positive charges are created on the surface of the rod.
d) positive charges are transferred from the silk to the rod.
e) positive charges are transferred from the rod to the silk.

18.2.2. Glass is a very good electrical insulator. How is then
possible that a glass rod can be charged by rubbing it with cloth?
a) When the rod is rubbed, it becomes an electrical conductor.
b) Although the rod is an insulator, any excess charge will slowly be
conducted away.
c) When the rod is rubbed, the part of the rod that is in contact with
the cloth becomes electrically conductive.
d) Because the rod is an insulator, the charge that is transferred to
the surface of the rod has difficulty moving.
e) None of the above answers are correct.

Section 3:
Conductors & Insulators

 Not only can electric charge exist on an object, but it can also
move through and object.
 Substances that readily conduct electric charge are called
electrical conductors.
 Materials that conduct electric charge poorly are called
electrical insulators.
Conductors and Insulators

Section 4:
Charging by Contact &
Induction

Charging by contact
 Electrons repel on another, so they spread out evenly in a
conducting material

Charging by Induction
 Bring charged object near a neutral conductor.
 Opposite charges are attracted, like charges repel
 Attach grounding wire to far side
• Repelled charge will spread out into the wire
 Disconnect wire, then remove charged object

Static Cling
 The negatively charged rod induces a slight positive surface
charge on the plastic or insulators.
 Charge can remain on surface and effect other objects

18.4.1. An initially electrically neutral conducting sphere is placed
on an insulating stand. A negatively-charged glass rod is brought
near, but does not touch the sphere. Without moving the rod, a
wire is then attached to the sphere that connects it to earth
ground. The wire, then the rod are removed. What is the final
charge on the sphere?
a) negative
b) positive
c) neutral
d) It has a fifty percent chance of having a positive charge and a fifty
percent chance of having a negative charge.

18.4.2. An initially electrically neutral conducting sphere is placed on an
insulating stand. A positively-charged glass rod is brought near, but
does not touch the sphere. Without moving the rod, a wire is then
attached to the sphere that connects it to earth ground. The wire, then
the rod are removed. The sphere is subsequently found to have a
negative charge. From the outcome and results of this experiment,
what can we conclude about the charging process?
a) Positive charges move freely from the sphere to the ground.
b) Negative charges move freely from the ground to the sphere.
c) Both positive charges and negative charges are moving freely.
d) More experimentation needs to be done before the sign of moving
charges can be determined.

18.4.3. Three identical conducting spheres on individual insulating stands are
initially electrically neutral. The three spheres are arranged so that they are in
a line and touching as shown. A negatively-charged conducting rod is brought
into contact with sphere A. Subsequently, someone takes sphere C away.
Then, someone takes sphere B away. Finally, the rod is taken away. What is
the sign of the final charge, if any, of the three spheres?
A B C
a) + + −
b) + − +
c) + 0 −
d) − + 0
e) − − −

18.4.4. Consider the conducting spheres labeled A, B, and C shown in the
drawing. The spheres are initially charged as shown on the left, then
wires are connected and disconnected in a sequence shown moving
toward the right. What is the final charge on sphere A at the end of the
sequence?
a) +Q
b) + Q/2
c) + Q/3
d) + Q/4
e) + Q/8

18.4.5. Consider the conducting spheres labeled A, B, and C shown
in the drawing. The spheres are initially charged as shown on
the left, then wires are connected and disconnected in a
sequence shown moving toward the right. What is the final
charge on sphere C at the end of the sequence?
a) +Q
b) + Q/2
c) + Q/3
d) +2Q
e) +3Q

Section 5:
Coulomb’s Law

2
21
r
qq
kF =
( ) 229
CmN1099.841 ⋅×== ok πε
( )2212
mNC1085.8 ⋅×= −
οε
Coulomb’s Law
 The magnitude of the electrostatic force exerted by one point
charge on another point charge is directly proportional to the
magnitude of the charges and inversely proportional to the
square of the distance between them.
2
21
r
qq
F ∝
εo called the permittivity of free space

Example 3 A Model of the Hydrogen
Atom
In the Bohr model of the hydrogen atom,
the electron is in orbit about the
nuclear proton at a radius of 5.29x10-11
m.
Determine the speed of the
electron, assuming the orbit to be circular.
2
21
r
qq
kF =
( )( )
( )211
219229
m1029.5
C1060.1CmN1099.8
−
−
×
×⋅×
=
cmaF =
mFrv =
N1022.8 8−
×=
rmv2
=
( )( )
kg109.11
m1029.5N1022.8
31-
118
×
××
=
−−
sm1018.2 6
×=

Example 4 Three Charges on a Line
Determine the magnitude and direction of the
net force on q1.
2
21
12
r
qq
kF =
2
31
13
r
qq
kF =
1312 FFF

+−=
( )( )( )
( )2
66229
m20.0
C100.4C100.3CmN1099.8 −−
××⋅×
= N7.2=
( )( )( )
( )2
66229
m15.0
C100.7C100.3CmN1099.8 −−
××⋅×
= N4.8=
N4.8N7.2 +−= 5.7N+=

18.5.1. Three insulating balls are hung from a wooden rod using thread. The three
balls are then individually charged via induction. Subsequently, balls A and
B are observed to attract each other, while ball C is repelled by ball B. Which
one of the following statements concerning this situation is correct?
a) A and B are charged with charges of opposite
signs; and C is charged with charge that has the
same sign as B.
b) A and B are charged with charges of the same
sign; and C is electrically neutral.
c) A is electrically neutral; and C is charged with charge that has the same sign as
B.
d) B is electrically neutral; and C is charged with charge that has the same sign as
A.
e) Choices a and c are both possible configurations.

18.5.2. Two objects separated by a distance r are each carrying a
charge −q. The magnitude of the force exerted on the second
object by the first is F. If the first object is removed and
replaced with an identical object that carries a charge +4q, what
is the magnitude of the electric force on the second object?
a) 4F
b) 2F
c) F
d) F/2
e) F/4

18.5.3. Two objects, A with charge +Q and B with charge +4Q, are
separated by a distance r. The magnitude of the force exerted
on the second object by the first is F. If the first object is
moved to a distance 2r from the second object, what is the
magnitude of the electric force on the second object?
a) zero newtons
b) 2F
c) F
d) F/2
e) F/4

18.5.4. Consider the two charges shown in the drawing. Which of the
following statements correctly describes the direction of the electric
force acting on the two charges?
a) The force on q1 points to the left and the force on q2 points to the left.
b) The force on q1 points to the right and the force on q2 points to the
left.
c) The force on q1 points to the left and the force on q2 points to the
right.
d) The force on q1 points to the right and the force on q2 points to the
right.

18.5.5. Consider the two charges shown in the drawing. Which of the
following statements correctly describes the magnitude of the electric
force acting on the two charges?
a) The force on q1 has a magnitude that is twice that of the force on q2.
b) The force on q2 has a magnitude that is twice that of the force on q1.
c) The force on q1 has the same magnitude as that of the force on q2.
d) The force on q2 has a magnitude that is four times that of the force on q1.
e) The force on q1 has a magnitude that is four times that of the force on q2.

18.5.6. Two point charges are stationary and separated by a
distance R. Which one of the following pairs of charges
would result in the largest repulsive force?
a) –2q and +4q
b) –3q and −2q
c) +3q and −2q
d) +2q and +4q
e) –3q and −q

18.5.7. A charged particle is located at the center of a uniformly charged hollow sphere.
What is the net electrostatic force on the charged particle?
a) The net electrostatic force on the particle will be zero newtons because all of the
charges on the sphere are either repelled or attracted to the particle, so they exert no
force on it.
b) The net electrostatic force on the particle will be zero newtons because the vector sum
of all of the forces on it due to the charges on the sphere is zero, so they exert no
force on it.
c) The net electrostatic force on the particle will be the least at the center, but its
magnitude will be greater than zero newtons.
d) The net electrostatic force on the particle will be positive if the particle and sphere
have opposite signs and negative if they have the same sign.
e) The net electrostatic force on the particle will be negative if the particle and sphere
have opposite signs and positive if they have the same sign.

18.5.8. A charged particle is located at a distance R/2 from the center of a uniformly
charged hollow sphere of radius R. What is the net electrostatic force on the
charged particle?
a) The net electrostatic force on the particle will be zero newtons because the vector
sum of all of the forces on it due to the charges on the sphere is zero, so they exert
no force on it.
b) The net electrostatic force on the particle will be larger than that which would be
exerted if the particle was at the center of the sphere.
c) The net electrostatic force on the particle will be smaller than that which would be
exerted if the particle was at the center of the sphere.
d) The net electrostatic force on the particle will be positive if the particle and sphere
have opposite signs and negative if they have the same sign.
e) The net electrostatic force on the particle will be negative if the particle and sphere
have opposite signs and positive if they have the same sign.

18.5.9. Three plates may be charged positively or negatively or be
electrically neutral. In the drawing shown, plate A is attracted by
both plates B and C. What occurs if plates B and C are brought
close together?
a) B and C would be attracted to one another.
b) B and C would be repelled by one another.
c) B and C would exert no force on each other.
d) There is too little information given to make a conclusion.

18.5.10. Three plates may be charged positively or negatively or be
electrically neutral. In the drawing shown, plate A is repelled by
both plates B and C. What occurs if plates B and C are brought
close together?
a) B and C would be attracted to one another.
b) B and C would be repelled by one another.
c) B and C would exert no force on each other.
d) There is too little information given to make a conclusion.

18.5.11. As shown in the drawing, a positively charged particle remains
stationary between particles A and B. The positively charged particle
is one-quarter the distance between the two other particles, as shown.
What can be concluded from the situation?
a) The charge on A must be four times as large as the charge on B.
b) The charge on A must be sixteen times as large as the charge on B.
c) The charge on A must be one-half as large as the charge on B.
d) The charge on A must be one-fourth as large as the charge on B.
e) The charge on A must be one-sixteenth as large as the charge on B.

18.5.12. Two particles are separated by a distance d. Particle A has a
charge +Q and particle B has a charge +3Q. At what distance
from particle A along the line connecting particles A and B
would you place a third charged particle such that no net
electrostatic force acts on it?
a) d/3
b) d/2
c) d/4
d) d/6
e) d/9

Section 6:
The Electric Field

Electric Fields
 It is often easier to think of natural forces as acting on an
object, than analyzing the force itself
 Gravity
• We use F = mg much more that we use F = Gm1m2 /r2
 The same is true for Electric forces
 We often look out how Coulomb’s law effects a small charge
• Just as with gravity we look at how a planet effects a small
mass
 We call the effect of a charge of a group of charges the
Electric Field
 We look at the effect of the electric forces present on a small
positive charge

 The positive charge experiences a force which is the vector
sum of the forces exerted by the charges on the rod and the
two spheres.
 This test charge should have a small magnitude so it doesn’t
affect the other charge.
Electric Fields

Example 6 A Test Charge
The positive test charge has a magnitude of
3.0x10-8
C and experiences a force of 6.0x10-8
N.
(a) Find the force per coulomb that the test charge
experiences.
(b) Predict the force that a charge of +12x10-8
C
would experience if it replaced the test charge.
oq
F(a)
(b) ( )( )C100.12CN0.2 8−
×=F
C100.3
N100.6
8
8
−
−
×
×
= CN0.2=
N1024 8−
×=

The electric field that exists at a point is the electrostatic force experienced
by a small test charge placed at that point divided by the charge itself:
oq
F
E


=
SI Units of Electric Field: newton per coulomb (N/C)
Definition of Electric Field

It is the surrounding charges that create the electric field at a given point.

Example 7 An Electric Field
Leads to a Force
The charges on the two metal
spheres and the ebonite rod
create an electric
field at the spot indicated. The
field has a magnitude of 2.0
N/C. Determine
the force on the charges in (a)
and (b)
EqF o=(a)
(b) EqF o=
( )( )C100.18CN0.2 8−
×= N1036 8−
×=
( )( )C100.24CN0.2 8−
×= N1048 8−
×=

Electric fields from different sources
add as vectors.
Electric Force in 2D

Example 10 The Electric Field of a Point
Charge
The isolated point charge of q=+15μC is
in a vacuum. The test charge is 0.20m
to the right and has a charge qo=+15μC.
Determine the electric field at point P.
2
21
r
qq
kF =
( )( )( )
( )2
66229
m20.0
C1015C1080.0CmN1099.8 −−
××⋅×
=F
oq
F
E =
N7.2=
C100.80
N7.2
6-
×
= CN104.3 6
×=

2
r
q
kE =
The electric field does not depend on the test charge.
o
o
qr
qq
k
1
2
=
Point charge qo:
The Electric Field Equation
oq
F
E = Test charge

Example 11 The Electric Fields from Separate Charges May Cancel
Two positive point charges, q1=+16μC and q2=+4.0μC are separated in a
vacuum by a distance of 3.0m. Find the spot on the line between the charges
where the net electric field is zero.
2
r
q
kE =
( ) ( )
( )2
6
2
6
m0.3
C100.4C1016
d
k
d
k
−
×
=
× −−21 EE =
( ) 22
m0.30.2 dd =−
m0.2+=d

Conceptual Example 12 Symmetry and the
Electric Field
Point charges are fixes to the corners of a rectangle in two
different ways. The charges have the same magnitudes
but different signs.
Consider the net electric field at the center of the rectangle
in each case. Which field is stronger?

Parallel plate
capacitor A
q
E
oε
=
( )2212
mNC1085.8 ⋅×= −
οε
charge density
The Parallel Plate Capacitor
oε
σ
=

18.6.1. A positively-charged object is released from rest in a region
containing a uniform electric field. Which one of the following
statements concerning the subsequent motion of the object is correct?
a) The object will remain motionless.
b) The object will accelerate to some constant speed and move in the
direction of the electric field.
c) The object will accelerate to some constant speed and move in the
direction opposite that of the electric field.
d) The object will experience a constant acceleration and move in the
direction of the electric field.
e) The object will experience a constant acceleration and move in the
direction opposite that of the electric field.

18.6.2. Two negatively-charged objects are located on the x axis, equally distant
from the origin as shown. Consider the electric field at the point P1. How
will that electric field change if a third object with a charge +q is placed at
point P2? Note: the point P2 is the same distance from the origin as the point
P1 and the magnitude of each of the charges is the same.
a) The magnitude of the electric field will
decrease by 25%.
b) The magnitude of the electric field will
increase by 25%.
c) The magnitude of the electric field will
decrease by 50%.
d) The magnitude of the electric field will increase by 50%.
e) The magnitude of the electric field will increase by 100%.

18.6.3. At a distance of one centimeter from an electron, the
electric field strength has a value E. At what distance is the
electric field strength equal to E/2?
a) 0.5 cm
b) 1.4 cm
c) 2.0 cm
d) 3.2 cm
e) 4.0 cm

Section 7:
Electric Field Lines

Electric field lines or lines of force provide a map of the
electric field in the space surrounding electric charges.
They show where a test charge (+) would be pushed.

Electric field lines are always directed away from positive charges and
toward negative charges.
-

Electric field lines always begin on a positive
charge and end on a negative charge and do
not stop in midspace.

The number of lines leaving a positive charge or entering a
negative charge is proportional to the magnitude of the charge.
+ -

Conceptual Example 13 Drawing Electric
Field Lines
There are three things wrong with part (a) of
the drawing. What are they?
 Number of field lines should be
proportional to the charge:
• 2q should have double the
lines of each of the q’s
 Field lines cannot cross
 Field lines will almost never be
parallel lines for point charges

18.7.1. Consider the drawing, where the solid lines with arrows
represent the electric field due to the charged object. An
electron is placed at the point P and released at rest. Which of
the following vectors represents the direction of the force, if
any, on the electron?

18.7.2. The plates of a parallel plate capacitor are connected to a
battery. Each plate has an area A. One plate has a net charge of
+q. What is the magnitude of the electric field outside the
capacitor? Note: ignore end effects at the edges of the capacitor.
a)
b)
c) ε0Aq
d) q
e) zero N/C
A
q 0ε
0εA
q

18.7.3. An electron traveling horizontally to the right enters a
region where a uniform electric field is directed downward.
What is the direction of the force exerted on the electron once it
has entered the field?
a) upward
b) downward
c) to the right
d) to the left
e) The force is zero newtons.

18.7.4. Consider the electric field lines shown in the drawing. Which of the
following statements correctly describes this situation?
a) The electric field is due to a
positively charged particle.
b) The electric field is due to a
negatively charged particle.
c) The electric field is due to a
positively charged particle and
a negatively charged particle.
d) The electric field is due to
particles that are both charged
either positively or negatively.

18.7.5. Consider the electric field lines shown in the drawing. Which of the
following statements correctly describes this situation?
a) A and B are both positively
charged particles.
b) A and B are both negatively
charged particles.
c) A is a positively charged
particle and B is a negatively
charged particle.
d) B is a positively charged
particle and A is a negatively
charged particle.

18.7.6. Four charges are located on the corners of a square as shown
in the drawing. What is the direction of the net electric field at
the point labeled P?
a) toward the upper left corner of the square
b) toward the middle of the right side
of the square
c) toward the middle of the bottom
side of the square
d) toward the lower right corner of the square
e) There is no direction. The electric field at P is zero N/C.
P

18.7.7. Four charges are located on the corners of a square as shown in the
drawing. What is the direction of the net electric field at the point
labeled P?
a) toward the upper left corner of the square
b) toward the middle of the right side
of the square (directly right)
c) toward the middle of the bottom side
of the square (directly down)
d) toward the lower right corner
of the square
e) There is no direction. The electric field at P is zero N/C.
P

18.7.8. A positively charged object is located to the left of a
negatively charged object as shown. Electric field lines are
shown connecting the two objects. The five points on the
electric field lines are labeled A, B, C, D, and E. At which one
of these points would a test charge experience the largest force?
a) A
b) B
c) C
d) D
e) E

shown connecting the two objects. The five points on the electric
field lines are labeled A, B, C, D, and E. At which one of these
points would a test charge experience the smallest force?
a) A
b) B
c) C
d) D
e) E

points would a test charge experience the largest force?
a) A
b) B
c) C
d) D
e) E

points would a test charge experience the smallest force?
a) A
b) B
c) C
d) D
e) E

Section 8:
The Electric Field Inside
a Conductor: Shielding

Charges Inside a
Conductor
 Electrons will repel each other equally.
 At equilibrium under electrostatic
conditions, any excess charge resides on
the surface of a conductor.
 At equilibrium under electrostatic
conditions, the electric field is zero at any
point within a conducting material.
 The conductor shields any charge within
it from electric fields created outside the
conductor.

The electric field just outside the surface of a conductor is perpendicular to
the surface at equilibrium under electrostatic conditions.
Field Lines Approaching a Conductor

Conceptual Example 14 A Conductor in
an Electric Field
A charge is suspended at the center of
a hollow, electrically neutral, spherical
conductor. Show that this charge induces
(a) a charge of –q on the interior surface
and
(b) a charge of +q on the exterior surface
of the conductor.

18.8.1. The drawing shows a hollow conducting sphere with a net
positive charge uniformly distributed over its surface. A small
negatively-charged object has been brought near the sphere as
shown. What is the direction of the electric field at the center of
the sphere?
a) There is no electric field at the center of the sphere.
b) to the left
c) to the right
d) upward
e) downward

Section 9:
Gauss’ Law
Not AP B

( )22
4 rqrkqE oπε==
( )oAqE ε=

o
q
EA
ε
=
EAE =Φflux,Electric
Gauss’ Law

( )∑ ∆=Φ AEE φcos
Gauss’ Law

GAUSS’ LAW
The electric flux through a Gaussian
surface is equal to the net charge
enclosed in that surface divided by
the permittivity of free space:
( )
o
Q
AE
ε
φ =∆∑ cos
SI Units of Electric Flux: N·m2
/C

Example 15 The Electric Field of a Charged Thin Spherical Shell
A positive charge is spread uniformly over the shell. Find the magnitude
of the electric field at any point (a) outside the shell and (b) inside the
shell.
( )
o
Q
AE
ε
φ =∆∑ cos
( ) ( )
( )2
4
0coscos
rEAE
AEAEE
π
φ
=∆=
∆=∆=Φ
∑
∑∑
( )
o
Q
rE
ε
π =2
4

( )
o
Q
rE
ε
π =2
4
(a) Outside the shell, the Gaussian
surface encloses all of the charge.
or
q
E
επ 2
4
=
(b) Inside the shell, the Gaussian
surface encloses no charge.
0=E
Example 15 cont’d

18.9.1. Gauss’ law may be written:
Which of the following statements concerning the charge q is true?
a) The charge q is the sum of all charges.
b) The charge q is the sum of all charges on the Gaussian surface.
c) The charge q is the sum of all charges inside the Gaussian surface.
d) The electric field due to q is zero inside the Gaussian surface.
0ε
φ
q
AEE =∆=Φ ∑ )cos(

18.9.2. When you calculate the electric flux through a Gaussian
surface, of what are you determining the flow through the
surface?
a) charge
b) electric current
c) electric energy
d) electric field
e) None of the above answers are correct.

18.9.3. Consider the five situations shown. Each one contains either a charge q or
a charge 2q. A Gaussian surface surrounds the charged particle in each case.
Considering the electric flux through each of the Gaussian surfaces, which of
the following comparative statements is correct?
a)
b)
c)
d)
e)
2 4 1 3Φ = Φ > Φ = Φ
1 3 2 4Φ = Φ > Φ = Φ
2 1 4 3Φ > Φ > Φ > Φ
3 4 2 1Φ = Φ > Φ = Φ
4 3 2 1Φ > Φ > Φ > Φ

18.9.4. When a particle with a charge Q is surrounded by a spherical
Gaussian surface, the electric flux through the surface is ΦS. Consider
what would happen if the particle was surrounded by a cylindrical
Gaussian surface or a Gaussian cube. How would the fluxes through
the cylindrical ΦCyl and cubic ΦCubic surfaces compare to ΦS?
a)
b)
c)
d)
e)
S Cubic CylΦ = Φ > Φ
S Cyl CubicΦ > Φ = Φ
S Cyl CubicΦ = Φ = Φ
S Cubic CylΦ < Φ < Φ
S Cubic CylΦ > Φ > Φ

18.9.5. A spherical Gaussian surface of radius R is surrounding a
particle with a net charge q. If the spherical Gaussian surface is
replaced by a cube, under what conditions would the electric flux
through the sides of the cube be the same as through the spherical
surface?
a) under all conditions
b) if the sides of the cube are of length R
c) if the sides of the cube are of length 2R
d) if the diagonals of the cube are of length 2R
e) under no conditions

Section 10:
Copiers & Computer Printers

Ch 18 Electric Fields

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (9)

Similar to Ch 18 Electric Fields

Similar to Ch 18 Electric Fields (20)

More from Scott Thomas

More from Scott Thomas (20)

Recently uploaded

Recently uploaded (20)

Ch 18 Electric Fields