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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 ppt slides + movies
Tutorial solutions
Multiple choice quizzes
Ancillary information Administration, syllabus, on-line study, academic honesty
Assessment
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)
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 (§31.1-31.6, 32.1, 32.3)
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Chapter 23
Electrostatics
Before we get started… just for fun…
What would happen if you could throw a ball at 0.9c?
Electricity and Magnetism,
Some Ancient History
Many applications
Macroscopic and microscopic
Chinese
Documents suggest that magnetism was observed
as early as 2000 BC
Greeks
Electrical and magnetic phenomena as early as
700 BC
Experiments with amber and magnetite
3
Electricity and Magnetism,
Some History, 2
1785
Charles Coulomb confirmed inverse
square law form for electric forces
1819
Hans Oersted found a compass needle
deflected when near a wire carrying an
electric current
Electricity and Magnetism,
Some History, 3
1831 Michael Faraday and Joseph Henry showed that
when a wire is moved near a magnet, an electric current is produced in the wire
1873 James Clerk Maxwell used observations and other
experimental facts as a basis for formulating the laws of electromagnetism
Unified electricity and magnetism
Electric Charges, 1
There are two kinds of electric charges
Called positive and negative 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
EFA02AN1
4
Demo EA3: Electrostatic forces
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
The rubber rod is
negatively charged
The glass rod is
positively charged
The two rods will
attract
Electric Charges, 3
The rubber rod is
negatively charged
The second rubber
rod is also
negatively charged
The two rods will
repel
5
More About Electric Charges
Electric charge is always conserved in
an isolated system
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
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
The electric charge, q, is said to be quantized
q is the standard symbol used for charge
Electric charge exists as discrete packets
q = Ne
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
Electrical conductors are materials in which some of the electrons are free electrons 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
6
Insulators
Electrical insulators are materials in which all of the electrons are bound to atoms 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
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.
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.
Quick Quiz 23.2
7
Conductors - charge distribution
EFM03VD2
Coulomb’s Law
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,
The SI unit of charge is the Coulomb (C)
ke is called the Coulomb constant
ke = 8.9875 x 109 N.m2/C2 = 1/(4πo)
o is the permittivity of free space
o = 8.8542 x 10-12 C2 / N.m2
Fe k
e
q1q
2
r2
Coulomb’s Law
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8
Coulomb’s Law
The force is attractive if the charges are of opposite sign
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 i.e. the same work is done whatever path is taken to
move between two positions
Fe k
e
q1q
2
r2
Coulomb's Law, Notes
Remember the charges need to be in Coulombs e is the smallest unit of charge
[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
Vector Nature of Electric
Forces
In vector form,
is a unit vector
directed from q1 to q2
Like charges produce a
repulsive force between
them
F12 k
e
q1q
2
r2
ˆ r
ˆ r
9
Vector Nature of Electrical
Forces, 2
Electrical forces obey Newton’s Third
Law
The force on q1 is equal in magnitude and
opposite in direction to the force on q2
F21 = -F12
With like signs for the charges, the
product q1q2 is positive and the force is
repulsive
Vector Nature of Electrical
Forces, 3
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
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 23.4
10
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
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.
Quick Quiz 23.5
Hydrogen Atom Example
The electrical force between the electron and
proton is found from Coulomb’s law
Fe = keq1q2 / r2 = 8.2 x 10-8 N (exercise….)
This can be compared to the gravitational
force between the electron and the proton
Fg = Gmemp / r2 = 3.6 x 10-47 N (exercise…)
The electric force is vastly stronger than the
gravitational force!
QuickTime™ and aGraphics decompressor
are needed to see this picture.
Strength Electrostatic Forces c.f. Gravity
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11
The Superposition Principle
The resultant force on any one charge
equals the vector sum of the forces
exerted by the other individual charges
that are present
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
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
Calculate the force for charges +q, +Q and -Q, distributed at the vertices of an equilateral triangle.
Electrical Force with
Gravitational Force; example
The spheres are in
equilibrium
Since they are separated,
they exert a repulsive
force on each other
Like charges
Equate the forces, since
they are in equilibrium
note that one force is an
electrical force and the
other is gravitational
12
Electrical Force with
Gravitational Forces; example
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
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: the number of lines per
unit area.
Electric Field – Definition
An electric field is said to exist in the
region of space around a charged
object
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
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
Strictly, only valid for a point charge
13
Electric Field Notes, Final
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
Remember Coulomb’s law, between the
source and test charges, can be
expressed as
Then, the electric field will be
2ˆo
e e
qqk
rF r
2ˆe
e
o
qk
q r
FE r
Superposition with Electric
Fields
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
2ˆi
e i
i i
qk
r E r
Superposition Example
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 Remember, the fields add
as vectors
The direction of the individual fields is the direction of the force on a positive test charge
14
Electric Field – Continuous
Charge Distribution
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
For the individual charge elements
Because the charge distribution is
continuous
2ˆ
e
qk
r
E r
2 20
ˆ ˆlimi
i
e i eq
i i
q dqk k
r r
E r r
Charge Densities
Volume charge density: when a charge is distributed evenly throughout a volume ρ = Q / V
Surface charge density: when a charge is distributed evenly over a surface area σ = Q / A
Linear charge density: when a charge is distributed along a line = Q / ℓ
Example – Charged Disk
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
Example 23.9
15
Electric Field Lines
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 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
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 This indicates the field is
non-uniform
Electric Field: van der Graaf generator
EFM05VD1
Demo EA14: van der Graaf generator
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.
16
Electric Field Lines, Positive
Point Charge
The field lines radiate
outward in all directions In three dimensions, the
distribution is spherical
The lines are directed
away from the source
charge A positive test charge would
be repelled away from the
positive source charge
Electric Field Lines, Negative
Point Charge
The field lines radiate
inward in all directions
The lines are directed
toward the source
charge
A positive test charge
would be attracted
toward the negative
source charge
Electric Field Lines – Dipole
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
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
17
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
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 23.7
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.
Answer: (b). Electric field lines begin and end on charges
and cannot close on themselves to form loops.
Quick Quiz 23.8
18
Motion of Charged Particles
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
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
The electron is projected
horizontally into a uniform
electric field
The electron undergoes a
downward acceleration
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
c.f. projectile motion under
gravity
End of Chapter
19
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
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 23.1
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
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).
Quick Quiz 23.6
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