Introduction to Physical Systems Dr. E.J. Zita, The Evergreen State College, 30.Sept.02 Lab II Rm 2272, Program syllabus, schedule, and details online at 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

Time budget Plus your presentations in fall, library research in winter, and advanced research in spring.

Introduction to Electromagnetism Dr. 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

Four fundamental forces

Four laws of electromagnetism

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 = A x B x + A y B y + A z B z = A B cos  Cross product: |AxB| = A B sin 

Examples of vector products Dot product: work done by variable force Cross product: angular momentum L = r x mv

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

Practice: 1.15: Calculate the divergence and curl of v = x 2 x + 3xz 2 y - 2xz z 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).

Sign up for your 20-minute presentations: 7 Oct: Vector Operations Vector Algebra Triple Products 14.Oct: Position, Displacement, and Separation Vectors Ordinary derivatives + Gradient 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? (R E =6.4 x 10 6 m) 2.12 (p.75) Find (and sketch) the electric field E(r) inside a uniformly charged sphere of charge density .