Introduction to Physical Systems Dr. E.J. Zita, The Evergreen State College, 30.Sept.02 Lab II Rm 2272, zita@evergreen.e

1. Introduction to Physical SystemsDr. E.J. Zita, The Evergreen State College, 30.Sept.02Lab II Rm 2272, zita@evergreen.edu, 360-867-6853 Program syllabus, schedule, and details online at http://academic.evergreen.edu/curricular/physys/0607 Zita@evergreen.edu, 2272 Lab II TA = Jada Maxwell

2. Introduction to ElectromagnetismDr. E.J. Zita, The Evergreen State College, 16.Jan.2007 • 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

3. 4 realms of physics, 4 fundamental forces

4. Four laws of electromagnetism

5. 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)

6. 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)

7. 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

8. Some advanced topics • Conservation laws • Radiation • waves in plasmas, magnetohydrodynamics • Potentials and Fields • Special relativity

9. Ch.1: Vector Analysis Dot product: A.B = Ax Bx + Ay By + Az Bz = A B cos q Cross product: |AxB| = A B sin q =

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

11. 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 Differential operator “del”

12. Practice: 1.15: Calculate the divergence and curl ofv = x2x + 3xz2y - 2xz z Ex: If v = E, then div E = charge; if v = B, then curl B = current.

13. 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).

14. 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)

15. Gauss’ Law practice: 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 r. 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).