Physics / Higher Physics 1B
Electricity and Magnetism
Administrative Details

Michael Ashley, m.ashley@unsw.edu.au
Room 137, OMB
My course website (linked from “lecturer’s notes” in
Moodle):
http://mcba11.phys.unsw.edu.au/~mcba/PHYS1231
Please ensure you have a “course pack”
Please bring your lab book next week
Moodle site for course information:
 http://moodle.telt.unsw.edu.au
 Lecture Notes
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ppt slides + movies
Tutorial solutions
Multiple choice quizzes
Ancillary information
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Administration, syllabus, on-line study, academic honesty
Assessment
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Laboratory 20%
Six quizzes 20% (due Sunday 11pm odd
weeks; beginning week 3)
End of Session exam 60%
You must pass each component and complete
all the labs
Syllabus (Physics for Scientists and
Engineers with Modern Physics, Serway &
Jewitt, 8th ed)
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Electrostatics (§23.1, 23.3-23.6)
Gauss’s Law (§24.1-24.4)
Electric Potential (§25.1-25.6, 25.8)
Capacitance & Dielectrics (§26.1-26.5)
Magnetic Fields & Magnetism (§29.1-29.4)
Ampere’s & Biot-Savart Law (§30.1-30.5)
Faraday’s Law, Induction, Inductance (§31.131.6, 32.1, 32.3)
Chapter 23
Electrostatics
Before we get started…
just for fun…
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What would happen if you could throw
a ball at 0.9c?
Electricity and Magnetism,
Some Ancient History
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Many applications
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Chinese
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Macroscopic and microscopic
Documents suggest that magnetism was observed
as early as 2000 BC
Greeks
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Electrical and magnetic phenomena as early as
700 BC
Experiments with amber and magnetite
Electricity and Magnetism,
Some History, 2
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1785
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Charles Coulomb confirmed inverse
square law form for electric forces
1819
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Hans Oersted found a compass needle
deflected when near a wire carrying an
electric current
Electricity and Magnetism,
Some History, 3
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1831
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Michael Faraday and Joseph Henry showed that
when a wire is moved near a magnet, an electric
current is produced in the wire
1873
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James Clerk Maxwell used observations and other
experimental facts as a basis for formulating the
laws of electromagnetism
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Unified electricity and magnetism
Electric Charges, 1
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There are two kinds of electric charges
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Called positive and negative
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Negative charges are the type possessed by
electrons
Positive charges are the type possessed by
protons
Charges of the same sign repel one
another and charges with opposite
signs attract one another
Charges in matter: the atom
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EFA02AN1
Demo EA3: Electrostatic forces
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Attraction of a
stream of water by a
charged rod
Demo EA1: Electrostatic
Charging by Friction – can
move large objects
Glass rubbed with silk will gain a positive
charge and plastic rubbed with fur a
negative charge. A metal rod will also
acquire a charge if rubbed with rubber
and held by an insulated handle.
Electric Charges, 2
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The rubber rod is
negatively charged
The glass rod is
positively charged
The two rods will
attract
Electric Charges, 3
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The rubber rod is
negatively charged
The second rubber
rod is also
negatively charged
The two rods will
repel
More About Electric Charges
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Electric charge is always conserved in
an isolated system
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For example, charge is not created in the
process of rubbing two objects together
The electrification is due to a transfer of
charge from one object to another
Conservation of Electric
Charges
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A glass rod is rubbed
with silk
Electrons are
transferred from the
glass to the silk
Each electron adds a
negative charge to the
silk
An equal positive
charge is left on the rod
Quantization of Electric
Charges
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The electric charge, q, is said to be quantized
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q is the standard symbol used for charge
Electric charge exists as discrete packets
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q = Ne
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N is an integer
e is the fundamental unit of charge
|e| = 1.6 x 10-19 C
Electron: q = -e
Proton: q = +e
Conductors
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Electrical conductors are materials in which
some of the electrons are free electrons
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Free electrons are not bound to the atoms
These electrons can move relatively freely through
the material
Examples of good conductors include copper,
aluminum and silver
When a good conductor is charged in a small
region, the charge readily distributes itself over the
entire surface of the material
Insulators
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Electrical insulators are materials in which all
of the electrons are bound to atoms
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These electrons cannot move freely through the
material
Examples of good insulators include glass, rubber
and wood
When a good insulator is charged in a small
region, the charge is unable to move to other
regions of the material
Semiconductors
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The electrical properties of
semiconductors are somewhere
between those of insulators and
conductors
Examples of semiconductor materials
include silicon and germanium
Quick Quiz 23.2
Three objects are brought close to each other, two at a time.
When objects A and B are brought together, they repel.
When objects B and C are brought together, they also repel.
Which of the following are true?
(a) Objects A and C possess charges of the same sign.
(b) Objects A and C possess charges of opposite sign.
(c) All three of the objects possess charges of the same sign.
(d) One of the objects is neutral.
(e) We would need to perform additional experiments to
determine the signs of the charges.
Quick Quiz 23.2
Answer: (a), (c), and (e). The experiment shows that A and
B have charges of the same sign, as do objects B and C.
Thus, all three objects have charges of the same sign. We
cannot determine from this information, however, whether
the charges are positive or negative.
Conductors - charge
distribution
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EFM03VD2
Coulomb’s Law
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Charles Coulomb
measured the
magnitudes of electric
forces between two
small charged spheres
He found the force
depended on the
charges and the
distance between them
Coulomb’s Law, Equation
Mathematically,
q1 q 2
Fe  k e 2
r
 The SI unit of charge is the Coulomb (C)
 ke is called the Coulomb constant
9 . 2 2
 ke = 8.9875 x 10 N m /C = 1/(4πo)

 o is the permittivity of free space
-12 C2 / N.m2
 o = 8.8542 x 10
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Coulomb’s Law
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EFM04AN1
Coulomb’s Law
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Fe  k e
q1 q 2
r
2
The force is attractive if the charges are of
opposite sign
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The force is repulsive
if the charges are of
like sign
The electrical behavior of electrons and
protons is well described by modelling them
as point charges
The electrical force is a “conservative” force
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i.e. the same work is done whatever path is taken to
move between two positions
Coulomb's Law, Notes
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Remember the charges need to be in
Coulombs
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e is the smallest unit of charge
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[except quarks….]
e = 1.6 x 10-19 C
So 1 C needs 1/e = 6.24 x 1018 electrons or
protons!
Typical charges can be in the µC range
Remember that force is a vector quantity
Demo Ea2: Electrostatic forces
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Vector Nature of Electric
Forces
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In vector form,
F12  k e
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q1 q 2
rˆ is a unit vector
r
2
rˆ
directed from q1 to q2
Like charges produce a
repulsive force between
them
Vector Nature of Electrical
Forces, 2
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Electrical forces obey Newton’s Third
Law
The force on q1 is equal in magnitude and
opposite in direction to the force on q2
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F21 = -F12
With like signs for the charges, the
product q1q2 is positive and the force is
repulsive
Vector Nature of Electrical
Forces, 3
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Two point charges are
separated by a
distance r
With unlike signs for
the charges, the
product q1q2 is
negative and the force
is attractive
Quick Quiz 23.4
Object A has a charge of +2 μC, and object B has a charge of
+6 μC. Which statement is true about the electric forces on
the objects?
(a) FAB = –3FBA
(b) FAB = –FBA
(c) 3FAB = –FBA
(d) FAB = 3FBA
(e) FAB = FBA
(f) 3FAB = FBA
Quick Quiz 23.4
Answer: (e). From Newton's third law, the electric force
exerted by object B on object A is equal in magnitude to the
force exerted by object A on object B.
Quick Quiz 23.5
Object A has a charge of +2 μC, and object B has a charge of
+6 μC. Which statement is true about the electric forces on
the objects?
(a) FAB = –3FBA
(b) FAB = –FBA
(c) 3FAB = –FBA
(d) FAB = 3FBA
(e) FAB = FBA
(f) 3FAB = FBA
Quick Quiz 23.5
Answer: (b). From Newton's third law, the electric force
exerted by object B on object A is equal in magnitude to the
force exerted by object A on object B and in the opposite
direction.
Hydrogen Atom Example
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The electrical force between the electron and
proton is found from Coulomb’s law
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This can be compared to the gravitational
force between the electron and the proton
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Fe = keq1q2 / r2 = 8.2 x 10-8 N (exercise….)
Fg = Gmemp / r2 = 3.6 x 10-47 N (exercise…)
The electric force is vastly stronger than the
gravitational force!
Strength Electrostatic Forces
c.f. Gravity
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EFA04AN1
QuickTime™ and a
Graphics decompressor
are needed to see this picture.
The Superposition Principle
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The resultant force on any one charge
equals the vector sum of the forces
exerted by the other individual charges
that are present
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The resultant force on q1 is the vector
sum of all the forces exerted on it by
other charges: F1 = F21 + F31 + F41 + …
Superposition Principle,
Example
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The force exerted by
q1 on q3 is F13
The force exerted by
q2 on q3 is F23
The resultant force
exerted on q3 is the
vector sum of F13 and
F23
Example
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Calculate the force for charges +q, +Q
and -Q, distributed at the vertices of an
equilateral triangle.
Electrical Force with
Gravitational Force; example
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The spheres are in
equilibrium
Since they are separated,
they exert a repulsive
force on each other
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Like charges
Equate the forces, since
they are in equilibrium
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note that one force is an
electrical force and the
other is gravitational
Electrical Force with
Gravitational Forces; example
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The free body
diagram includes the
components of the
tension, the electrical
force, and the weight
Solve for |q|
You cannot
determine the sign of
q, only that they both
have same sign
Demo EA5: Electrostatic field
and lines of force
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Paper strips attached to
a van der Graaf
generator show the
electrostatic field lines;
i.e. the direction of the
electric field.
Think about the inverse
square law:
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the number of lines per
unit area.
Electric Field – Definition
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An electric field is said to exist in the
region of space around a charged
object
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This charged object is the source charge
When another charged object, the test
charge, enters this electric field, an
electric force acts on it
Electric Field – Definition, cont
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The electric field is defined as the electric
force on the test charge per unit charge
The electric field vector, E, at a point in space
is defined as the electric force F acting on a
positive test charge, qo placed at that point
divided by the test charge: E = Fe / qo.
i.e. Fe = q0 E
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Strictly, only valid for a point charge
Electric Field Notes, Final
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The direction of E is that
of the force on a positive
test charge
The SI units of E are N/C
We can also say that an
electric field exists at a
point in space if a test
charge at that point
experiences an electric
force
Electric Field, Vector Form
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Remember Coulomb’s law, between the
source and test charges, can be
expressed as
Fe  k e
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qq o
r
rˆ
2
Then, the electric field will be
E
Fe
qo
 ke
q
r
2
rˆ
Superposition with Electric
Fields
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At any point P, the total electric field due
to a group of source charges equals the
vector sum of electric fields of all the
charges
E  ke 
i
qi
ri
2
rˆi
Superposition Example
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Find the electric field at
point P due to q1, E1
Find the electric field at
point P due to q2, E2
E = E1 + E2
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Remember, the fields add
as vectors
The direction of the
individual fields is the
direction of the force on a
positive test charge
Electric Field – Continuous
Charge Distribution
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Divide the charge
distribution into small
elements, each of which
contains Δq
Calculate the electric field
due to one of these
elements at point P
Evaluate the total field by
summing the contributions
of all the charge elements
Electric Field – Continuous
Charge Distribution, equations
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For the individual charge elements
E  ke
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q
r
2
rˆ
Because the charge distribution is
continuous
E  k e lim
qi  0

i
qi
ri
2
rˆi  k e 
dq
r
2
rˆ
Charge Densities
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Volume charge density: when a charge is
distributed evenly throughout a volume
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Surface charge density: when a charge is
distributed evenly over a surface area
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ρ=Q/V
σ=Q/A
Linear charge density: when a charge is
distributed along a line
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=Q/ℓ
Example – Charged Disk
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The ring has a radius R
and a uniform charge
density σ
Choose dq as a ring of
radius r
The ring has a surface
area 2πr dr
Calculate E-field at P a
distance x away on axis
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Example 23.9
Electric Field Lines
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Field lines give us a means of representing
the electric field pictorially
The electric field vector E is tangent to the
electric field line at each point
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The line has a direction that is the same as that of
the electric field vector
The number of lines per unit area through a
surface perpendicular to the lines is
proportional to the magnitude of the electric
field in that region
Electric Field Lines, General
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The density of lines
through surface A is
greater than through
surface B
The magnitude of the
electric field is greater on
surface A than B
The lines at different
locations point in different
directions
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This indicates the field is
non-uniform
Electric Field:
van der Graaf generator
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EFM05VD1
Demo EA14: van der Graaf
generator
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Electric field, and lines of force, shown
in a hair-raising experiment!
With clean hair, the subject’s hair will
stand on end as it becomes charged.
Electric Field Lines, Positive
Point Charge
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The field lines radiate
outward in all directions
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In three dimensions, the
distribution is spherical
The lines are directed
away from the source
charge
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A positive test charge would
be repelled away from the
positive source charge
Electric Field Lines, Negative
Point Charge
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The field lines radiate
inward in all directions
The lines are directed
toward the source
charge
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A positive test charge
would be attracted
toward the negative
source charge
Electric Field Lines – Dipole
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The charges are
equal and opposite
The number of field
lines leaving the
positive charge
equals the number
of lines terminating
on the negative
charge
Electric Field Lines – Like
Charges
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The charges are equal
and positive
The same number of
lines leave each
charge since they are
equal in magnitude
At a great distance,
the field is
approximately equal to
that of a single charge
of 2q
Quick Quiz 23.7
Rank the magnitude of the electric field at points A, B, and C
shown in this figure (greatest magnitude first).
(a) A, B, C
(b) A, C, B
(c) B, C, A
(d) B, A, C
(e) C, A, B
(f) C, B, A
Quick Quiz 23.7
Answer: (a). The field is greatest at point A because this is
where the field lines are closest together. The absence of
lines near point C indicates that the electric field there is
zero.
Quick Quiz 23.8
Which of the following statements about electric field lines
associated with electric charges is false?
(a) Electric field lines can be either straight or curved.
(b) Electric field lines can form closed loops.
(c) Electric field lines begin on positive charges and end on
negative charges.
(d) Electric field lines can never intersect with one another.
Quick Quiz 23.8
Answer: (b). Electric field lines begin and end on charges
and cannot close on themselves to form loops.
Motion of Charged Particles
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When a charged particle is placed in an
electric field, it experiences an electrical
force
If this is the only force on the particle, it
must be the net force
The net force will cause the particle to
accelerate according to Newton’s
second law
Motion of Particles, cont
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Fe = qE = ma
If E is uniform, then a is constant
If the particle has a positive charge, its
acceleration is in the direction of the
field
Electron in a Uniform Field,
Example
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The electron is projected
horizontally into a uniform
electric field
The electron undergoes a
downward acceleration
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It is negative, so the
acceleration is opposite E
F=ma=qE so that a=qE/m
Its motion is parabolic while
between the plates
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c.f. projectile motion under
gravity
End of Chapter
Quick Quiz 23.1
If you rub an inflated balloon against your hair, the two
materials attract each other, as shown in this figure. Fill in
the blank: the amount of charge present in the system of the
balloon and your hair after rubbing is _____ the amount of
charge present before rubbing.
(a) less than
(b) the same as
(c) more than
Quick Quiz 23.1
Answer: (b). The amount of charge present in the isolated
system after rubbing is the same as that before because
charge is conserved; it is just distributed differently.
Quick Quiz 23.6
A test charge of +3 μC is at a point P where an external
electric field is directed to the right and has a magnitude of 4
× 106 N/C. If the test charge is replaced with another test
charge of –3 μC, the external electric field at P
(a) is unaffected
(b) reverses direction
(c) changes in a way that cannot be determined
Quick Quiz 23.6
Answer: (a). There is no effect on the electric field if we
assume that the source charge producing the field is not
disturbed by our actions. Remember that the electric field is
created by source charge(s) (unseen in this case), not the test
charge(s).