Introduction to Physical Systems Dr. E.J. Zita, The Evergreen State College, 30.Sept.02 Lab II Rm...
-
date post
20-Dec-2015 -
Category
Documents
-
view
215 -
download
0
Transcript of Introduction to Physical Systems Dr. E.J. Zita, The Evergreen State College, 30.Sept.02 Lab II Rm...
Introduction to Physical SystemsDr. E.J. Zita, The Evergreen State College, 30.Sept.02Lab II Rm 2272, [email protected], 360-867-6853
Program syllabus, schedule, and details online at http://academic.evergreen.edu/curricular/physys2002/home.htm
Monday: E&M in homeroom = Lab II Rm 2242
Tuesday: DiffEq with Math Methods and Math Seminar (workshop on WebX in CAL tomorrow at 5:00 - photos today)
Wed: office hours
Thus: Mechanics and Physics Seminar in homeroom
TA = Noah Heller ([email protected])
Time budget
E&M DiffEq Mechanics Total time5 hrs class 5 hrs class 5 hrs class 154 hrs reading 4 hrs reading 4 hrs reading 126 hrs homework 6 hrs homework 6 hrs homework 18
46 minimum
Plus your presentations in fall, library research in winter, and advanced research
in spring.
Introduction to ElectromagnetismDr. E.J. Zita, The Evergreen State College, 30.Sept.02
• 4 realms of physics• 4 fundamental forces• 4 laws of EM• statics and dynamics• conservation laws• EM waves• potentials• Ch.1: Vector analysis• Ch.2: Electrostatics
Four realms of physics
Classical Mechanics(big and slow:
everyday experience)
Quantum Mechanics(small: particles, waves)
Special relativity(fast: light, fast particles)
Quantum field theory(small and fast: quarks)
Four laws of electromagnetism
Electric Magnetic
Gauss' Law
Charges make E fields
Gauss' Law
No magnetic monopoles
Ampere's Law
Currents make B fields(so does changing E)
Faraday's Law
Changing B make E fields
Electrostatics
• Charges make E fields and forces
• charges make scalar potential differences dV
• E can be found from V• Electric forces move
charges• Electric fields store
energy (capacitance)
Magnetostatics
• Currents make B fields• currents make magnetic
vector potential A• B can be found from A
• Magnetic forces move charges and currents
• Magnetic fields store energy (inductance)
Electrodynamics
• Changing E(t) make B(x)• Changing B(t) make E(x)• Wave equations for E and B
• Electromagnetic waves• Motors and generators• Dynamic Sun
Advanced topics
• Conservation laws
• Radiation
• waves in plasmas
• Potentials and Fields
• Special relativity
Ch.1: Vector Analysis
Dot product: A.B = Ax Bx + Ay By + Az Bz = A B cos
Cross product: |AxB| = A B sin zyx
zyx
BBB
AAA
zyx
zB y B x B ,zA yA xA zyxzyx BA
Examples of vector products
Dot product: work done by variable force
Cross product:
angular momentum
L = r x mv
dlFW cos
Differential operator “del”
Del differentiates each component of a vector.
Gradient of a scalar function = slope in each direction
Divergence of vector = dot product = what flows out
Curl of vector = cross product = circulation
yz
yy
xx
ˆˆ
y
fz
y
fy
x
fxf
ˆˆ
y
Vz
y
Vy
x
Vx zyx
ˆˆV
zyx
VVVzyx
zyx
zyx
ˆˆV
Practice: 1.15: Calculate the divergence and
curl of v = x2 x + 3xz2 y - 2xz z
...)2(
ˆ)3(
ˆ22
y
xzz
y
xzy
x
xx
V
zyx
xzxzxzyx
zyx
ˆˆ
222
V
Ex: If v = E, then div E = charge; if v = B, then curl B = current.
Separation vector differs from position vector:
Position vector = location of a point with respect to the origin.
Separation vector: from SOURCE (e.g. a charge at position r’) TO POINT of interest (e.g. the place where you want to find the field, at r).
222ˆˆˆ zyxrzzyyxx r
222 )'()'()'('
ˆ)'(ˆ)'(ˆ)'('
zzyyxx
zzzyyyxxx
rr
rr
Sign up for your 20-minute presentations:
7 Oct: 1.1.1 Vector Operations
1.1.2 Vector Algebra
1.1.3 Triple Products
14.Oct: 1.1.4 Position, Displacement, and Separation Vectors
1.2.1 + 1.2.2 Ordinary derivatives + Gradient
1.2.3 The Del Operator
Ch.2: Electrostatics: charges make electric fields
• Charges make E fields and forces
• charges make scalar potential differences dV
• E can be found from V• Electric forces move
charges• Electric fields store
energy (capacitance)
Gauss’ Law practice:
2.21 (p.82) Find the potential V(r) inside and outside this sphere with total radius R and total charge q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V(r).
What surface charge density does it take to make Earth’s field of 100V/m? (RE=6.4 x 106 m)
2.12 (p.75) Find (and sketch) the electric field E(r) inside a uniformly charged sphere of charge density .