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Introduction to Physical Systems Dr. E.J. Zita, The Evergreen State College, 30.Sept.02 Lab 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 - PowerPoint PPT Presentation
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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 fundamental forces
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 .