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Unformatted text preview: 3/29/10 PHYSICS 1C
LECTURE 1
Vahé Peroomian PHYSICS 1C ELECTRODYNAMICS, OPTICS,
AND SPECIAL RELATIVITY
Mondays, Tuesdays, Wednesdays, and Fridays at 1:00 P.M.
Kinsey Pavilion 1220B Instructor:
Dr. Vahé Peroomian Office: 3860 Slichter Hall
Phone: (310) 8254114
Email: vahe@igpp.ucla.edu Text: University Physics, Young and Freedman, 12th Edition OFFICE HOURS
Mondays, Tuesdays and Wednesdays,
2:00 pm – 3:00 pm and by appointment
Hours will be conducted in 3850 Slichter
Hall Office 1 3/29/10 TEACHING ASSISTANT
Lauren Pearce
Email: lpearce@physics.ucla.edu
Office Hours: TBA EXAMS
First Midterm
Monday, April 19, 2010 In class
Second Midterm
Monday, May 17, 2010 In class
Final Exam
Thursday, June 10, 2010
11:30 am – 2:30 am
EXAM POLICIES
For both midterms and the final you will need your
student I.D. One 4” × 6” sheet of notes, in your own
handwriting, will be allowed during exams. Makeup exams will not be given. If you miss a
midterm, then the grading percentages of the other
midterm and the final exam will be adjusted to 30%
and 60%, respectively. This will only occur if and
only if I receive a medical excuse letter signed by a
physician. You cannot miss the final exam!!!! Midterm exam grades will be in terms of points and
percentages; letter grades will not be assigned. 2 3/29/10 HOMEWORK
Homework will be done/turned in through the
Mastering Physics website,
http://www.masteringphysics.com
If you did not receive a Mastering Physics access
code with your textbook, you can purchase one
from the Mastering Physics website.
You will need to enroll in my course, ID#
PEROOMIAN1CS10
Each homework assignment will consist of a
number of practice selftutoring problems and 10
graded problems.
Homework #1 is available now, and is due by
Wednesday, April 7, 11:59pm. GRADING
Homework
Midterm #1
Midterm #2
Final Exam
Total
10%
20%
20%
50%
100% CLASS WEBSITE
http://ccle.ucla.edu/course/view.php?name=10SPHYSICS1C1
(go to www.physics.ucla.edu, click on “physics,” then “classes”
and on “1C”)
Check class website frequently for:
Homework assignments
PDFs of my lecture PowerPoints
Sample exams, etc. Class website will be updated later today with HW
#1. 3 3/29/10 HELPFUL HINTS
PDF of PowerPoints used in class posted to class
website.
Many of the examples in my lectures are not from
our textbook. Make sure you do all the textbook
examples!!!
If you do homework in a group, please make sure
you know how to do each problem individually.
When studying for exams, don’t be satisfied with
just redoing the problems I did in class plus
homework. The more extra problems you do, the
better. EXTRA HELP
Aside from my office hours and the TA’s office
hours, extra help is available through the Physics
98 workshop program run by Brent Corbin.
The workshop for this course meets Mondays and
Wednesdays from 3:00 pm  4:30 pm
(starting week 2).
To attend the workshop, you need to enroll in
Physics 98XB Lab 3, a 1 unit P/NP course (with
no impact on unit total), which will also give you
access to the 98X website where you can get
worksheets, solutions, good informational
handouts, chatroom access, etc. A QUICK REVIEW OF SOME
CHAPTER 27 CONCEPTS
Vahé Peroomian 4 3/29/10 MAGNETIC FORCE ON A
CURRENTCARRYING CONDUCTOR
The magnetic force on a straight
wire segment is given by: F= I l ×B
Magnetic force on infinitesimal
wire section: dF = I d l × B EXAMPLE 27.7
A straight horizontal copper rod carries a current
of 50.0 A from west to east in a region between the
poles of a large electromagnet. In this region there
is a horizontal magnetic field toward the northeast
(45° north of east) with magnitude 1.20 T.
(a) Find the magnitude and direction of the force
on a 1.00 m section of rod.
(b) While keeping the rod horizontal, how should
it be oriented to maximize the magnitude of the
force? What is the force magnitude in the
case? EXAMPLE 1
A wire bent into a semicircle of radius R forms a
closed circuit and carries a current I. The wire lies
in the xy plane, and a uniform magnetic field is
directed along the positive y axis. Find the
magnitude and direction of
the magnetic force acting on
the straight portion of the
wire and on the curved
portion. 5 3/29/10 FORCE AND TORQUE
ON A CURRENT LOOP
The net force on a current loop in a uniform
magnetic field is zero. However, the net torque
is not in general equal to zero. THE MAGNETIC DIPOLE MOMENT
The magnetic dipole moment (µ) is the
magnetic analog of the electric dipole moment
(Chapter 21). For a loop of N turns, µ = NIA TORQUE AND POTENTIAL ENERGY
The vector torque on a current loop is given by τ = µ×B
Potential energy for a magnetic dipole is given
by: U = − µ ⋅ B = − µ B cos φ 6 3/29/10 EXAMPLE 2
A rectangular coil of dimensions 5.40 cm × 8.50
cm consists of 25 turns of wire and carries a
current of 15.0 mA. A 0.350T magnetic field is
applied parallel to the plane of the coil.
(a) Calculate the magnitude of the magnetic dipole
moment of the coil.
(b) What is the magnitude of the torque acting on
the loop? EXAMPLE 3
Consider the loop of wire in the figure. Imagine it is pivoted along side
4, which is parallel to the z axis and fastened so that side 4 remains
fixed and the rest of the loop hangs vertically in the gravitational field
of the Earth but can rotate around side 4 (panel b). The mass of the loop
is 50.0 g, and the sides are of lengths a = 0.200 m and b = 0.100 m. The
loop carries a current of 3.50 A and is immersed in a vertical uniform
magnetic field of magnitude 0.010 0 T in the positive y direction (panel
c). What angle does the plane of the loop make with the vertical? CHAPTER 28
SOURCES OF
MAGNETIC FIELD
Vahé Peroomian 7 3/29/10 HOW ARE MAGNETIC FIELDS CREATED
A point charge q moving with constant
velocity v creates a vector magnetic field: µ qv × r
ˆ
B= 0
4π r 2
B= µ0 q v sin φ
4π
r2 PERMEABILITY OF FREE SPACE
The constant µ0 is called the “permeability of
free space,” and has the value µ0 = 4π × 10 −7 T ⋅ m/A
Relationship between µ0 and ε0: c2 = 1
ε 0 µ0 MAGNETIC FIELD OF
A CURRENT ELEMENT
The total magnetic field caused by several
moving charges is the vector sum of the
fields caused by the individual charges µ0 Idl × r
ˆ
dB =
4π r 2
BiotSavart Law
µ
B= 0
4π ∫ ˆ
Idl × r
2
r 8 3/29/10 MAGNETIC FIELD OF
A LONG STRAIGHT WIRE
The field near a long, straight currentcarrying conductor is given by
B= µ0 I
4π a ∫ (x −a B= 2 x dy
+ y 2 ) 3/ 2 µ0 I
2π r EXAMPLE 1
Consider a thin, straight wire carrying
a constant current I and placed along
the x axis as shown in the figure.
Determine the magnitude and
direction of the magnetic field at
point P due to this current. EXAMPLE 2
Consider a circular wire loop of radius a located in
the yz plane and carrying a steady current I as in
the figure. Calculate the magnetic field at an axial
point P a distance x from the center of the loop. 9 3/29/10 EXAMPLE 28.4
Two long straight parallel wires in the z direction,
perpendicular to the xy plane, each carry a current
I in opposite directions.
(a) Find the magnitude and direction of B at points
P1, P2, and P3.
(b) Find the magnitude and direction of B at any
point on the xaxis on the right of wire 2 in
terms of the xcoordinate of the point. FORCE BETWEEN
PARALLEL CONDUCTORS
The force per unit length between two
long, parallel, currentcarrying conductors
is given by
F µ II ′
L = 0 2π r THE AMPERE
When the magnitude of the force per unit
length between two long, parallel wires
that carry identical currents and are
separated by 1 meter is 2 × 10–7 N/m, the
current in each wire is defined to be 1
Ampere. 10 3/29/10 EXAMPLE 4
Two infinitely long, parallel wires are lying on the ground a
distance a = 1.00 cm apart as shown in the figure. A third wire,
of length L = 10.0 m and mass 400 g, carries a current of I1 =
100 A and is levitated above the first two wires, at a horizontal
position midway between them. The infinitely long wires carry
equal currents I2 in the same direction, but in the direction
opposite that in the levitated wire. What current must the
infinitely long wires carry so that the three wires form an
equilateral triangle? EXAMPLE: MAGNETIC FIELD OF
A CIRCULAR CURRENT LOOP
Consider a circular wire loop of radius a located
in the yz plane and carrying a steady current I.
Calculate the magnetic field at an axial point P a
distance x from the center of the loop. MAGNETIC FIELD ON THE
AXIS OF A COIL
What is the magnetic field along the axis of a
coil with N circular loops? Bx = µ0 NIa 2
2 ( x 2 + a 2 ) 3/ 2 Bx = µ0 NI
2a 11 3/29/10 AMPERE’S LAW
Analogous to Gauss’s Law for electric
fields, evaluates the line integral of B
around a closed path. the Magnetic Field B.dl
∫ = µ0 I enclosed ere r , R . Here the current I 9 passing through the plane of circle 2 is less than circle 2 to
t he area pr 2
l area pR 2 of the pr 2
Ir
5
I
pR 2 ES
S XAMPLE 5
r2
C B ? d s 5 B 1 2pr 2 5 m0I r 5 m0 a R 2 I b Ir 5 r2
I
R2 A long, straight wire of radius R carries a steady current I that
is uniformly distributed through the cross section of the wire.
m0 I
Calculate the magnetic field a distance r from the center of the
for nd r ≤
(
B 5 ire in the2 regions(r ≥ Rr a, R) R.
w a 2pR b r .) the wire is identiB
t he case in highly
Figure . (Example 30.5)
use Ampère’s law
Br
Magnitude of the magnetic field
.1). The magnetic
B 1/r
versus r for the wire shown in Figto the expression
ure 30.13. The field is proportional
harged sphere (see
to r inside the wire and varies as 1/r
r
g netic field versus
R
outside the wire.
re 30.14. Inside the
ions 30.14 and 30.15 give the same value of the magnetic field at r 5 R , demonous at the surface of the wire. gnetic Field Created by a Toroid E
en used to create an almostXAMPLE 28.9
area. The device consistsA solenoid consists of a helical winding of wire on a cylinder,
of
S
S
Loop 1
ds B
(a torus) made of a nonconusually circular in crosssection. There can be hundreds or
thousands of closelyspaced turns,
losely spaced turns of wire,
ea
n occupied by the torus, ach of which can be regarded as a
circular loop. Use Ampere’s Law to
r
find the field at or near the center of
such a long solenoid. The solenoid
b
has n turns of wire per unit length and
c
a
carries a current I.
I lly to understand how the
orus could be a solid matepped into the shape shown
gh degree of symmetry, we
aw problem.
loop (loop 1) of radius r in
t he magnitude of the field
S
S
t, so B ? d s 5 B ds. Furthert imes, so the total current I Loop 2 Figure . (Example 30.6) A toroid consisting of many turns of wire. If the turns are closely
spaced, the magnetic field in the interior of the
toroid is tangent to the dashed circle (loop 1) and
v aries as 1/r. T he dimension a is the crosssectional
r adius of the torus. The field outside the toroid is
very small and can be described by using the amperian loop (loop 2) at the right side, perpendicular
to the page. 12 3/29/10 EXAMPLE 6
A device called a toroid is often used to create an almost
uniform magnetic field in some enclosed area. The device
consists of a conducting wire wrapped around a ring (a torus)
made of a nonconducting material. For a toroid having N
closely spaced turns of wire,
calculate the magnetic field
in the region occupied by the
torus, a distance r from the
center. 13 ...
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This note was uploaded on 06/03/2011 for the course PHYSICS 1c taught by Professor Peroomian during the Spring '10 term at UCLA.
 Spring '10
 peroomian
 Physics, Special Relativity

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