MAGNETIC FORCE & MAGNETIC FIELD (Chapter 22)
Read historical background in 22.1
Magnetism known of for over 2000 years.
Magnets known to have two poles
o North points to Earths North Pole (which is a south magnetic pole!)
o South points to Earths South
ELECTRIC POTENTIAL AROUND A POINT CHARGE
The work done by an external force (i.e. you?) to move charge q from A B :
Equals change in potential energy of the charge
B
U qVB V A q E ds
A
Sign OK? Yes.
o Says if it takes positive work to move charge, pote
MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR (22.5)
Important: basis of electric motors, microphones, speakers, transducers, etc.
For wire carrying current I upward
q
v
o
d is upwards for each charge
o Force on EACH CHARGE points left
(perpendicular to
GAUSSS LAW FOR SYMMETRIC CHARGE DISTRIBUTIONS (19.10)
Recall Gausss Law:
qinside
e E dA
0
over
closed
surface
dA is a vector normal to surface with magnitude equal to the area of the surface
element
How do we use Gausss Law? Two Ways:
qinside
e
0
o re
ELECTRIC FIELDS DUE TO CONTINUOUS CHARGE DISTRIBUTIONS
Approach:
Break charge distribution into small elements (treat each as a point charge)
Write vector sum of contributions from elements
Take limit as elements become infinitesimally small INTEGRAL
S
ELECTRIC POTENTIAL AT THE SURFACE OF AND INSIDE CHARGED
CONDUCTORS (text section 20.6)
For a charged conductor:
Any excess (net) charge MUST be at the surface
There can be no component of E parallel to the surface
o Means that E just outside a conductor
Getting Electric Field E from Electric Potential V (IMPORTANT)
Useful because V is a scalar and superposition does not require vector sum
V
E
ds
Start by noting:
B
implies dV E ds
A
E due to a point charge (radial electric field)
only nonzero te
INTERFERENCE DUE TO THIN FILMS (27.4,27.5 in text)
c
n
Index of refraction
v:
important property of transparent material
o c is the speed of light in vacuum (or air)
o v is the speed of light in the transparent material
o n > 1 for most transparent materi
HOW DO MAXWELLS EQUATIONS GIVE RISE TO ELECTROMAGNETIC
WAVES? (SKETCH ONLY)
y
Faradays Law:
dB
E
d
s
dt
around
gives
loop 1
Amperes Law:
d E
B
d
s
0 0
d t gives
around
loop 2
E
B
x
t
E
1
(Eq.1)
x
z
B
E
0 0
x
t
2
(Eq. 2)
B
Take derivatives of Eqs. 1 a
ELECTRIC POTENTIAL (Chapter 20)
In mechanics, saw relationship between conservative force and potential energy:
Fx
dU
dx
Says: How scalar quantity (potential energy) depends on position gives
components of a vector quantity (force)
Any connection to elec
AMPERES LAW (22.9 in text)
Amperes law: relates magnetic field around a closed path to current through a
surface bounded by that path
Useful for calculating B only in case of high symmetry
o Similar tool for magnetic fields that Gausss law is for electri
CONDUCTORS IN ELECTROSTATIC EQUILIBRIUM (19.11)
Properties are a result of the following:
In a good conductor, electrons are free to move.
At electrostatic equilibrium, charges MUST feel no force OR ELSE they will
move until there is no force
One result
EXAMPLE (based on problem 75 from page 655)
A solid insulating sphere of radius a is uniformly charged with a total charge Q. It
is surrounded by an concentric uncharged conducting spherical shell with an
inner radius b and an outer radius c.
(a) Find the
Oscillations: Review (Chapter 12)
Oscillations: motions that are periodic in time (i.e. repetitive)
o Swinging object (pendulum)
o Vibrating object (spring, guitar string, etc.)
o Part of medium (i.e. string, water) as wave passes by
Oscillation requ
Simple and Physical Pendula
Simple Pendulum: point mass m on massless string L
How do we find natural frequency ?
o Use Newtons 2nd law to get differential equation for SHM
o Identify from differential equation
Forces on hanging mass:
o For strin
Sinusoidal Traveling Waves (13.2 in text)
For any traveling wave, expect y x, t f x vt
o Ask: what is the form of function f for a sinusoidal wave with:
specific speed v
specific wavelength
First: look at x dependence of sinusoidal wave funct
ELECTRIC FIELD LINES (19.6)
There is an electric field vector for every point in
space around a charge
Electric field fills space around charge.
Can REPRESENT E in a region of space by Electric Field Lines (EFL)
RULES for drawing/interpreting Electric Fi
ELECTRIC FORCE (Chapter 19)
Electric forces are important
All interatomic and intermolecular forces are electric
o i.e. forces that determine properties of materials
Two kinds of charge: positive (+) and negative (-)
opposite charges attract, like charg
Waves transport energy:
Mechanical waves:
o propagating disturbance (from equilibrium) of medium
E
Electromagnetic waves (i.e. light, radio, etc.):
o Propagate without medium
B
MECHANICAL WAVES (Chapter 13)
Concepts to watch for:
o Types of wa
SUPERPOSITION PRINCIPLE (14.1 in text):
When two waves meet in a medium effects add
Resultant disturbance is sum of combining disturbances
o y R x, t y1 x, t y 2 x, t
INTERFERENCE OF SINUSOIDAL TRAVELING WAVES
First: two waves, both going right, identi
ELECTRIC FLUX (section 19.8)
Electric flux is a quantity proportional to the number of electric field lines (EFL)
passing through a given area.
Will define more precisely
Very important concept. Will use to relate electric field to charge.
1st step: Def
ELECTRIC FIELD (Section 19.5)
Electric fields due to point charges for now (will do more later)
Imagine an arrangement of point
charges in space
Force on a small positive charge q3 at P
Force on a small negative charge q4 at P
Dont need a different vector
STANDING WAVES IN AN AIR COLUMN (Wind Instruments)
Sound waves (longitudinal) reflect from open and closed tube ends
Two possible boundary conditions
Can also describe wave in terms of PRESSURE or DISPLACEMENT
AT A CLOSED TUBE END
No longitudinal dis
WHAT DOES ELECTRIC FLUX THROUGH A CLOSED SURFACE TELL US
ABOUT THE CHARGE ENCLOSED BY THE SURFACE
Electric field lines:
start on positive charges
end on negative charges
For a CLOSED surface around a volume of space:
the NET number of Electric Field Li
SOUND (Longitudinal) WAVES
Imagine planes of atoms in tube of air
As sound wave passes, each plane oscillates along direction of propagation
Can represent as displacement of air or pressure change (90 out of phase)
Wave function for sound
Can write i
Physics 1051 - Fall 2012. Test #2.
NAME
STUDENT NUMBER
09th November 2012
Time: 50 min
Instructor: Dr. Ania Harlick
INSTRUCTIONS
1. There are four questions, each worth 12.5 points in total. Answer all the questions,
show all your workings.
2. The amount
Physics 1051 - Fall 2011. Test #1.
NAME
STUDENT NUMBER
October 14,2011
Time: 50 min
Instructor: Dr. Ania Harlick
INSTRUCTIONS
1. There are four questions, each consisting of short theory part and a problem solving
part. Answer all the questions
2. The amo
Physics 1051 - Fall 2011. Test #2.
NAME
STUDENT NUMBER
November 2,2011
Time: 50 min
Instructor: Dr. Ania Harlick
INSTRUCTIONS
1. There are four questions, each consisting of short theory part and a problem solving
part. Answer all the questions.
2. The am