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3. Electromagnetic Theory
3.1. Electricity

3.1.1. Electric Forces <CJ chap 18.1-18.5 >
3.1.1.1.Discussion
3.1.1.1.1. We are all familiar with static electricity, lightning, and electrical currents from an early age.
3.1.1.1.2. Today we are familiar with the sources of charge: electrons, protons, ions, and atomic structure.
3.1.1.1.2.1.What is electrical charge? We do not really know – it is an intrinsic property like mass.
3.1.1.1.3. Electric charges are + & - Like charges (++ and - -) repel while opposites (+ -) attract.
3.1.1.1.3.1.Benjamin Franklin (1706-1790) defined charge & related it to lightning
3.1.1.1.4. Charges are quantized in integer multiples of the basic charge e = 1.6E-19 C
3.1.1.1.4.1.Robert Milliken proved this in 1909 and measured the charge on the electron e-
3.1.1.1.5. Electric charge is measured in units of Coulombs
3.1.1.1.6. The total electric charge in a closed domain is conserved
3.1.1.1.7. Conductors allow charges to move freely. Other materials are called insulators.
3.1.1.1.8. Coulombs law discovered 1785 By Charles Coulomb using a torsion balance to determine Fc
3.1.1.1.9. Electric Induction Charging – a conductor attached to the ground is ‘grounding’ / Contact charging
3.1.1.1.10. Linear Superposition: electrical (and magnetic) forces are (vectorially) additive from individual forces

3.1.1.2.Mathematical
3.1.1.2.1. Coulombs Law for forces between charges:
3.1.1.2.1.1.F1-2 = keq1 q2 / r2 where ke = 9E9 = 1/(4pe0) exactly = 8.9875 E9
3.1.1.2.1.2.The constant e0 is the permittivity of the vacuum
3.1.1.2.1.3.Force F is measured in Newtons
3.1.1.2.1.4.Charge per unit volume r = Q/V, per unit area s = Q/A, & per length l = Q/l
3.1.1.2.2. Problems with two charges
3.1.1.2.3. Vector problems with multiple charges

3.1.1.3.Advanced
3.1.1.3.1. Vector Statement of Coulomb’s Law
3.1.1.3.1.1.F1->2 = keq1 q2 (r2-r1) / |r2-r1|3 where F and r are vectors
3.1.1.3.2. Generally the force on a charge q from other charges is Fq(r) = q SI qi (r-ri) / |r-ri|3 thus:
3.1.1.3.3. E(r) = Si qi (r-ri) / |r-ri|3 = Fq(r) /q
3.1.1.3.4. E has units of Newtons / Coulomb (there is no special name for this unit)
3.1.1.3.5. Vector problems