Post on 13-Aug-2020
transcript
http://www.physics.umanitoba.ca/~birchall/PHYS1030/1Friday, January 11, 2008
2Friday, January 11, 2008
Schedule up to midterm break
3Friday, January 11, 2008
PHYS 1030, General Physics II
J. Birchall: 205 Allen, 474–6205 birchall@physics.umanitoba.ca
Office hours: Mondays 9:30 – 10:30, Tuesdays 1:30 - 2:30 Other times by appointment
Textbook: Cutnell & Johnson, 7th edition. Editions 6 and 5 also OK, although problem numbers sometimes differ.
Physics 1030 Lab Manual (2008) from bookstore
Scientific Calculator: mostly OK, but storage of notes and formulae or remote communication not allowed in tests and exams.
Web Pagewww.physics.umanitoba.ca/~birchall/PHYS1030
4Friday, January 11, 2008
Administration of course
• Coordinator: Dr. J. Birchall, keeper of the marks,
lab exemptions (if 80% average in PHYS 1030 lab in
last 2 years), room 205, Allen building, 474-6205
• Labs: Dr. H. Kunkel, in charge of labs.
Reschedule tests, labs (during week of test or lab),
room 402G, Allen building, 474-9214
• Tutorial tests: Dr. W. Ens/Dr. J. van Lierop
• Miscellaneous questions, problems: Physics main
office, room 301, Allen building
• Other – see the course handout or me
5Friday, January 11, 2008
Evaluation: Labs 20%Tutorial tests 10%Mastering Physics 5%Term Test 20% (Thursday, March 6, 7 – 9 pm)Final Exam 45% (April exam period)
Term test and final exam: Multiple choice, closed book, formula sheet provided. The final exam must be written to receive credit for the course.
Tutorial tests (4): Multiple choice, following a tutorial, closed book, no formula sheet. Must take the tutorial tests, even if you have a lab exemption.
Labs (5): Begin next week. No mark for labs if more than one lab missed without valid reason!
PHYS 1030, General Physics II
6Friday, January 11, 2008
“Mastering Physics”
Web-based homework assignments. Instant feedback, hints
point you to the solution.
About 5 assignments for credit for the whole course.
Worth 5% of final grade.
Experience from PHYS 1020: if you are using Windows
Vista, use Firefox, not Internet Explorer.
You can use your Mastering Physics username and password
from PHYS1020, but must use the new access code.
7Friday, January 11, 2008
• These notes:
www.physics.umanitoba.ca/~birchall/PHYS1030/lectures.html
• Publisher’s web site for worked problems, interactive problems, simulations...
www.wiley.com/college/cutnell
• “Crisis centre” – room 105, Allen building
More Help
8Friday, January 11, 2008
Overview of the Course
Electricity and Magnetism• Electric and magnetic fields and forces, electromagnetism• Electric circuits
Light and Optics• Electromagnetic waves, light – light rays: optics, optical instruments – light as a wave: interference, diffraction
Special Relativity• Special nature of light speed – special relativity
Modern Physics• Quantum physics – particles as waves, waves as particles• The atom, the nucleus, radioactive decay
9Friday, January 11, 2008
Chapter 18:
Electric Fields &
Forces
10Friday, January 11, 2008
Chapter 18: Electric Forces and Fields
• Electric charge, conservation of charge, electric force
• Conductors, insulators, flow of charge
• Coulomb’s law
• Electric field, electric field lines
• Electric field inside a conductor
• Omit 18.9, Gauss’ Law
11Friday, January 11, 2008
Unlike charges attract
Two types of charge, ‘+’ and ‘–’
Like charges repel
12Friday, January 11, 2008
Charge is Conserved
Charge is a property of many elementary particles (electrons, protons...), which they carry in multiples of a basic unit, “e”.
The charge of the electron is -e and +e for the proton.
– As charge is contained on the elementary particles in a fixed amount, charge is conserved.– Charges can be moved from one place to another, but the total charge is unchanged.
Charging by friction (eg, static build-up in winter, charging a balloon)
– charges flow from one surface to another – net charge is unchanged! – the force between charges is given by Coulomb’s law
13Friday, January 11, 2008
Charging by contact
(electrical conductor)→ charge of same
sign as on the rod
14Friday, January 11, 2008
Charging by induction
→ charge of opposite sign as on the rod
15Friday, January 11, 2008
(electrical insulator)
Charges contained on molecules of
the plastic
16Friday, January 11, 2008
Electrical Conductors
– charges (electrons) are free to move inside the conductor– flow of charge is an electric current
Electrical Insulators
– charges do not move freely
Similarities with flow of heat...
17Friday, January 11, 2008
Conduction of charge
Rate of flow of heat:
Rate of flow of charge:
Conduction of heat
I =!A
L!V
Q =kA
L!T
k = thermal conductivity
σ = electrical conductivity
18Friday, January 11, 2008
Coulomb’s Law
The force between two charges: F =kq1q2
r2
k = Coulomb’s constant = 9!109 N.m2/C2
Charges, q1, q
2 in Coulombs (C)
= 1/4!"0
(Coulomb, electrostatic force)
19Friday, January 11, 2008
Gravitational force
F =Gm1m2
r2masses always positive, force always attractive
but anti-matter...?
Electrostatic force
F =kq1q2
r2 charges positive or negative, force attractive or repulsive
20Friday, January 11, 2008
Electric Field
q q0
Test charge, q0P
!F
The force on the test charge at P is:
The electric field at P is defined by:
F =kqq0
r2
r
E =F
q0=kq
r2
!E =!F
q0, or, !F = q0!E
E =kq
r2due to the charge q
= force per unit charge
Coulomb’s law
21Friday, January 11, 2008
Electric field due
to many charges
Electric Field : !E =!F
q0
Each component of the force exerted on q0 is proportional to q0
! !E is the same for all values of q0
22Friday, January 11, 2008
Electric Field: !E =!Fq0
, or !F = q0!E
23Friday, January 11, 2008
The electric field at P is the vector sum of the electric fields due to the charge distributions at A and B
24Friday, January 11, 2008
Electric field lines from a positive charge
The closer together the field lines, the stronger the field
25Friday, January 11, 2008
26Friday, January 11, 2008
Electric Dipole
27Friday, January 11, 2008
Two positive charges
E = 0
28Friday, January 11, 2008
29Friday, January 11, 2008
Electric field lines ⇒ the direction of the
force on a positive test charge
• field lines point away from positive charges• point toward negative charges• the closer together the lines, the stronger the electric field
30Friday, January 11, 2008
Field lines do not cross – they
represent the direction of the force
on a positive test charge. The force
cannot point in two directions at
the same place!
The number of field lines reaching
a charge should be proportional to
the charge – the larger the charge,
the greater the electric field and the
larger the number of field lines.
Drawing field linesIncorrect
Correct
31Friday, January 11, 2008
Electric Field
!E =!F
q0, where !F is the force on a test charge q0
E =kq
r2at a distance r from a charge q
!0 = “permittivity of free space”
k =1
4!"0= 9!109 N.m2/C2
E =q
!0Abetween parallel charged plates
F =kqq0
r2, Coulomb’s law for force between charges q,q0
e= 1.6!10"19 C, magnitude of electron charge
(Newtons/Coulomb,
N/C)
= Coulomb constant
(from Coulomb’s law)
32Friday, January 11, 2008
Prob. 18.27: A ball (mass = 0.012 kg) carries a charge of –18 !C. What electric field is needed to cause the ball to float above the ground?
What is the weight of the ball?
What magnitude and direction of electric field supplies an equal upward force?
mg
!F = q!E
q = –18 !C m = 0.012 kg
33Friday, January 11, 2008
The story so far...
Charge is a property of certain elementary particles, such as electrons, protons. They each have a fixed amount of charge and so charge is conserved.
The effect of charge is the electrostatic (Coulomb) force. Like charges repel, unlike charges attract.
The force between charges is given by Coulomb’s law:
F = kqq0/r2,
charges q, q0 in Coulombs (C),
k = Coulomb constant = 9x109 N.m2/C2.
34Friday, January 11, 2008
Coulomb’s Law, Electric Field
q q0
Test charge, q0P
!Fr
The force on the test charge at P is:
The electric field at P is defined by:
(Coulomb’s law)
!E =!F
q0
F =kqq0
r2
Electric field lines point away from
positive a charge, toward a negative
charge
E =kq
r2 (due to q)
35Friday, January 11, 2008
Prob. 18C11: Three point charges are fixed to the corners of a square, one to a corner, in such as way that the net electric field at the empty corner is zero.
Do these charges all have
a) the same sign?
b) the same magnitude, but possibly different signs?
36Friday, January 11, 2008
18.C9: On a thin, nonconducting rod, positive charges are spread evenly, so that there is the same amount of charge per unit length at every point.
On another identical rod, positive charges are spread evenly over only the left half, and the same amount of negative charge is spread evenly over the right half.
For each rod, deduce the direction of the electric field at a point that is located directly above the midpoint of the rod.
Pair off charges on equal sections of the rod equidistant from the midpoint.
Work out the direction of the field from the paired-off charges.
37Friday, January 11, 2008
Where should q1 to placed so that the net force on it is zero?
Draw in the forces on q1 due to q2 and q3
Find where the forces are equal in magnitude and opposite in direction
When F = 0, the electric field due to q2 and q3 is also zero
q1
q2 q3L
38Friday, January 11, 2008
Prob. 18.29/30: Where is the electric field equal to zero?
Let point P be a guess for where E = 0, a distance x from the charge at
the left.
q1 = –16 !C q2 = +4 !CL = 3 m
Px 3 – x
E = 0 ?
39Friday, January 11, 2008
• Conductor contains charges that are free to move (electrons)
• At equilibrium, the charges are at rest
Electrical Conductor
E = 0
⇒ there can be no electric field inside the conductor, otherwise the
charges would be moving under the influence of the field and would not be in equilibrium.
The electric fields due to the rod and the charges on the surface cancel each other out inside the conductor
40Friday, January 11, 2008
E = 0
The extra electrons are pushed to the surface of the conductor by the
repulsive Coulomb forces between them.
As the electrons end up at equilibrium (i.e. at rest) there can be no electric
field inside the conductor, otherwise the electrons would still be moving...
Put some extra electron charges inside the conductor
Electrical Conductor
41Friday, January 11, 2008
E =q
!0A
Coulomb constant, k =1
4!"0
Uniform field inside a parallel plate capacitor
+q -q
Area A
!E
Uniform spacing of field
lines means constant
electric field
42Friday, January 11, 2008
At equilibrium, electric field lines are made to hit the conductor at right angles – charges have moved around the surface until they reached an equilibrium in which there is no longer a field parallel to the surface to move them further.
Uniform spacing of field lines means constant electric field
E = 0
Distortion of field lines due to charges on surface of conductor
–e E=0
43Friday, January 11, 2008
Equipotential SurfaceAs the electric field lines are at right angles to the conducting surface, no work is done in moving an electron charge around the surface
→ the electron has constant
potential energy on the surface
→ the surface is an “equipotential
surface” (more in chapter 19)
– equipotential surfaces are at right angles to electric field lines
Electric potentials are measured in volts (V).
–eE = 0
44Friday, January 11, 2008
Equipotentials and electric field
V1 volts
V2 volts
90º
90º 90º
90º
45Friday, January 11, 2008
Experiment 1 : Equipotential Lines
Sketch out equipotential lines by using a voltmeter to find places that lie at the same potential (voltage).
– one probe of the voltmeter is fixed in position, the other is moved around to locate points that give the same voltage reading on the voltmeter.
– all of the points giving the same reading on the voltmeter lie on an equipotential line.
Electric field lines are sketched in so that they are always at right angles to the equipotential lines.
46Friday, January 11, 2008
Interior of the cavity is shielded from outside fields – basis of “Faraday cage”
– example, shielding of electronic circuits (in a closed metal box) from stray
electric fields
Net charge = 0
Scooped out cylindrical conductor
47Friday, January 11, 2008
Mastering Physics
The first assignment is now available
It is due Friday, January 25 at 11 pm
Based on chapter 18
4 questions, each worth 10 marks
Have avoided questions where formulae have to be entered
or objects have to be dragged into boxes
Can use your PHYS 1020 (or Chemistry...) username and password
but must enter new Mastering Physics access code
48Friday, January 11, 2008
Click here, then “Yes, look me up” to enter old Mastering Physics username and password. Course ID is PHYS1030UM
www.masteringphysics.com
49Friday, January 11, 2008
Click for access code
50Friday, January 11, 2008
Inside an Electrical Conductor
Charges (electrons) are free to move, so that:
• forces between charges push charges to the surface of the conductor
• charges move around the surface until they come to equilibrium
• as the charges are at rest, there must be zero force acting on them
→ the electric field inside the conductor must be zero
• as the charges are at equilibrium, electric field lines
must hit the conductor at right angles, otherwise
charges would be moved around the surface
→ no work is done in moving charges around the surface
→ charges on the surface must have constant potential energy
→ the surface of the conductor is an “equipotential”
E = 0
e-
51Friday, January 11, 2008
Inside an Electrical Insulator
Electric charges cannot move, so:
→ charges do not move around to reduce the electric field to zero
→ an electric field can exist inside an insulator
52Friday, January 11, 2008
The number of field lines leaving +q is
equal to the number hitting the inner
surface of the conductor...
→ there must be an induced charge
of –q on the inner surface of the
conductor (the field lines point
toward the inner surface, so the
induced charge must be negative).
As the outer surface has a charge +q, it must have the same number of lines
leaving the surface
→ from the outside, the conductor has no effect on the electric field.
–q
+q
As the conductor is electrically neutral (has zero
net charge), there must also be an induced charge
+q on the outer surface of the conductor.
E = 0
Charge +q placed inside an
uncharged hollow conductor
53Friday, January 11, 2008
18.65/37: A proton is moving parallel to a uniform electric field. The electric field accelerates the proton and thereby increases its linear momentum to 5x10-23 kg.m/s from 1.5x10-23 kg.m/s in a time of 6.3 !s. What is the magnitude of the electric field?
54Friday, January 11, 2008
Prob. 18.68/22: Two small, identical objects are 0.2 m apart. Each carries a charge and they attract each other with a force of 1.2 N.
The objects are brought into contact so that the net charge is shared equally, and then they are returned to their initial positions. There is now a repulsive force of 1.2 N between the objects.
What is the initial charge on each object?
Write down Coulomb’s law for charges q1 and q2
Apply conservation of charge to find the charge q on each object after the charges have equalized
Write down Coulomb’s law again
55Friday, January 11, 2008
Prob. 18.24: There are four charges, each of magnitude 2 !C. Two are positive and two are negative.
The charges are fixed to the corners of a 0.3 m square, one to a corner, in such a way that the net force on any charge is directed to the centre of the square.
Find the magnitude of the electrostatic force experienced by any charge.
Work out how to arrange the four charges so that the net force on each is toward the centre of the square –"implies there must be some symmetry in the arrangement of charges.
56Friday, January 11, 2008
18.45: Two point charges of the same magnitude but opposite signs are fixed to either end of the base of an isosceles triangle. The electric field at the midpoint M between the charges has a magnitude EM. The field at point P has magnitude EP.
The ratio of these two field magnitudes is EM/EP = 9.0. Find the angle αin the diagram.
LL
dd
cos ! =d
L
57Friday, January 11, 2008
Prob. 18.19/67: Two small spheres are mounted on identical horizontal springs and rest on a frictionless table.
When the spheres are uncharged, the spacing between them is 0.05 m, and the springs are unstrained.
When each sphere has a charge of +1.6 !C, the spacing doubles.
Determine the spring constant, ks, of the springs.
58Friday, January 11, 2008
18.42: An electron enters the lower left side of a parallel plate capacitor
and exits at the upper right, as shown. The initial speed of the electron is
7#106 m/s. The capacitor is 2 cm long, the plates are 0.15 cm apart.
Find the magnitude of the electric field between the plates, assuming that
it is uniform everywhere.
F = –eE
vx = constantx
y
59Friday, January 11, 2008
Inkjet Printer
60Friday, January 11, 2008
Photocopy Machine
61Friday, January 11, 2008