Transcript Lecture #2 08/31/07

Announcements: Tutorials
Tutorials:
Monday 6-8pm Ryan Best
Tuesday 4:30-6:30pm Christine Carlisle
Wednesday 4:30-6:30pm Christine Carlisle
Thursday 6-8pm Ryan Best
Tentatively Olin 103
Learning Assistance Center:
[email protected]
Has done group tutoring before for Phy 113
.
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Announcements: Labs and Webassign
Buy the lab manual
Lab’s start next week.
Sections A-C are virtually full, section D is
nearly empty.
Webassign
3 people didn’t do the reading quiz for
today.
Note, I often comment on reading
quizzes.
registration requires an access code
online or bookstore
2
Recap
When
due?due?
Suppose
a plane
flies
100 miles NW.
Whenare
arehomeworks
reading
quizzes
A)
A) MWF
MWF7am
7am
What
is the displacement of the
B)
B) MWF
MWF10pm
10pm
plane?
C)
C) TR
TR7am
7am
D)
A)70.7
x + 70.7 y
D) FF10pm
10pm
B) -70.7 x + 70.7 y
C) 100 x
D)100 y
Vector Multiplication
There are two ways (in 2 or 3D) to multiply vectors.
Scalar product -> two vectors make a scalar
A ●B =N
Also called the dot product
or the inner product
Vector product -> two vectors make a vector
AxB=C
Also called the cross product,
alternating product or the
outer product
Scalar Product
Scalar product -> two vectors make a scalar
A ●B =ABcos q
A ●B =axbx+ayby+azbz
Geometric
Algebraic
Vector Product
Vector product -> two vectors make a vector
AxB=C
Geometric
C has magnitude absinq. Direction perpendicular
to the plane containing A and B.
A x B = (aybz-byaz)i+(azbx-bzax)j+(aAlgebraic
xby-bxay)k
The right hand rule
Force F
velocity v
Magnetic
Field B
F=q(v x B)
Electricity and Magnetism
•One of the four fundamental forces of nature
•Responsible for the vast majority of what we observe around us
•Probably best-understood and best-tested of the forces of nature
Electromagnetic Interactions:
•Electricity and Electronics
•Magnetism
•Chemistry
•Biology
• and even more
Electrical Charges
•Electric forces only affect objects with charge
•Charge is measured in Coulombs (C). A Coulomb is a large unit of
charge. 1 electron has -1.6 x 10-19 C of charge.
•Charge comes in both positive and negative quantities
•Charge is conserved – it can neither be created nor destroyed
•Charge is usually denoted by the letter q.
An object has a total charge of 5 mC. It is divided
into two pieces, one of which has charge 8 mC
and the other of which has charge
A) 3 mC
B) -3 mC
C) 13 mC
D) Such a division is impossible
Matter and Charges
•All matter is made of positive and negative charges (or neutral)
•An object’s total charge is very close to zero
•When an object becomes charged, a tiny fraction of its charged
particles (usually electrons) are lost or gained
•These particles (usually electrons) can flow through objects
What do you think of when you hear the
words conductor or insulator?
Conductor
A material that allows
electrons or other
charged particles to flow
freely
Insulator
A material that resists
the flow of electrons and
other charged particles
Elementary Charge
•Charges exist in integer multiples of a fundamental charge unit
called e
•We will consider e to be a positive number (some sources treat it as
negative)
e = 1.602  10-19 C
the magnitude of the charge on an electron. the
charge on a proton
When you write that an atom or molecule has a
charge +1 , you mean +e. A partial charge
means that a charge density can be modeled as
having a charge at a location less than e
Charge Densities
Charge can be localized to discrete points (point charges), or it
may be spread out over a volume, a surface or a line
•Charge density  units C/m3
•Surface charge density  units C/m2
•Linear charge density  units C/m
A cube with side 1 cm has a charge density
of  = 1 C/m3. What is the charge of the
cube?
A) 1 C
B) 0.01 C = 10 mC
C) 10-4 C = 100 m C
1 cm
D) 10-6C = 1 mC
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Coulomb’s Law
•Like charges repel, unlike charges attract
•Force is directly along a line joining the two charges
q1
ke q1q2
Fe 
rˆ
2
r
q2
r
q1q2
Fe 
rˆ
2
4 0 r
0 = 8.85410-12 C2/ (N●m2)
•Permittivity of free space
•An inverse square law, just like gravity
•Can be attractive or repulsive – unlike gravity
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•Constant is enormous compared to gravity
Coulomb’s Law: Applied
A Helium nucleus (charge +2e) is separated from one of its
electrons (charge –e) by about 3.00  10-11m. What is the force the
nucleus exerts on the electron? Is it attractive or repulsive?
ke q1q2
9 Nm2/C2
k
=
8.98810
Fe 
e
2
r
-11m the force on the electron
rHow
= just
3.00

10
We
calculated
from the
q1 =of3.204
 10-19C
does the acceleration
the nucleus
compare
nucleus.
does this
q2 =compare
-1.602 with
10-19the
C force
to that ofHow
the electron?
theacceleration
nucleus from
the nucleus
electron?is larger
A) on
The
of the
A)
on themN
nucleus
is twiceisassmaller
big
The
acceleration
of the Attractive
nucleus
FB)e=The
- force
0.513
Force
B)
The
force
on
the
nucleus
is
half
as
big
C) The accelerations are equal.
C) The forces are equal in magnitude
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Newton’s Laws and Kinematics
Fnet  ma
Newton’s laws and all
the kinematics you
learned in 113 are still
true!
F12   F21
t'
t'
dx
dv
v  ;a 
 v   adt  vt0 ; x   vdt  x0
dt
dt
t0
t0
If a does not depend on
time, then
1 2
v  at  v 0 ; x  at  v 0 t  x 0
2
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