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ELECTROMAGNETISM N

ELECTROMAGNETISM N. Alan Murray. Coulomb's Law Gauss's Law Potential Laplace's Equation Capacitance Biot-Savart Law Ampere's Law. Curl ( L ) Faraday's Law Inductance Descriptive only Waves in Free Space Reflection & Standing Waves. Syllabus. ® Maxwell's Equations. DON'T PANIC!.

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ELECTROMAGNETISM N

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  1. ELECTROMAGNETISMN Alan Murray

  2. Coulomb's Law Gauss's Law Potential Laplace's Equation Capacitance Biot-Savart Law Ampere's Law Curl (L) Faraday's Law Inductance Descriptive only Waves in Free Space Reflection & Standing Waves Syllabus ®Maxwell's Equations Alan Murray – University of Edinburgh

  3. DON'T PANIC! Maxwell's Equations … This is where we are heading … Alan Murray – University of Edinburgh

  4. Electromagnetism is hard Electromagnetism is irrelevant to modern electronics Electromagnetism is very boring I'm afraid that it is rather tricky Don't be silly, it is fundamental to everything I will do my best to render it otherwise! analogies minimised maths worked examples song and dance act Electromagnetic Mythsand Realities Alan Murray – University of Edinburgh

  5. Electromagnetism ...Some reassurance • Full understanding is possible for mathematically- and conceptually- "strong" students • Sufficient understanding • (in terms of usefulness and exam-passing) • is possible for all • There are around 6 possible exam questions! • this is only slightly flippant Alan Murray – University of Edinburgh

  6. These notes Your own additions to these notes i.e. listen actively and annotate the notes Kraus ("Electromagnetics", McGraw-Hill) essential purchase for 3rd and 4th year Formula Sheet ... provided in exam room “Worked examples” A Formula Sheet?!?! Resources Alan Murray – University of Edinburgh

  7. Assumed Knowledge • Charge, Voltage, Current • Q = CV • V = RI and its at-a-point vector equivalent,J = σEsee revision later • E = ρJ • ρ = 1/σ • E = V/d (but we will show that is only occasionally true!)Not much more! Alan Murray – University of Edinburgh

  8. Coulomb’s Law Alan Murray

  9. Remember … • Like charges repel one another • Opposite charges attract one another • The force of repulsion/attraction get weaker as the charges are farther apart. Alan Murray – University of Edinburgh

  10. â Qa Qb r Fa Fb Fa =-QaâQb 4per2 Fb =+QbâQa 4per2 Charges and Forces NB .. In air, e= 8.85 x 10-12 Fm-1 |â| = 1, Fa = -Fb Alan Murray – University of Edinburgh

  11. â3 1 unit â4 â1 â2 Unit vector âr? These are all unit vectors, |âi| = 1 They have a direction, and a magnitude of 1 â adds direction to a quantity without changing its magnitude e.g.... speed = 100m/s is a speed S 100(1/Ö2, 1/Ö2, 0)m/s is a velocityv =Sâ , 100m/s, North-East (ì) â = (1/Ö2, 1/Ö2, 0) in this case. Example on board! Alan Murray – University of Edinburgh

  12. Where Eb =-Qbâ 4per2 Fa =-QaâQb 4per2 Fb =+QbâQa 4per2 Where Ea= +Qaâ 4per2 Charges and Fields Fa =+QaEb Fb =+QbEa Eb(r) is the electric field set up by charge b at distance r (point a) Ea(r) is the electric field set up by charge a at distance r (point b) Alan Murray – University of Edinburgh

  13. Qa Qb Two Positive and equal charges |E| |Ea| |Eb| Alan Murray – University of Edinburgh

  14. d ------ + +++++ +q F E 0 V Voltage V Charges and Fields E = -V/d F = +q(-V/d) F = qE again Where E is the field set up inside the capacitor Alan Murray – University of Edinburgh

  15. V 0 |E| 0 Charges and Fields V E = -V/d Alan Murray – University of Edinburgh

  16. +Qc +Qd -Qe +Qa -Qb Several Charges? Ea Eb Ec Ed Ee Alan Murray – University of Edinburgh

  17. +Qc +Qd -Qe +Qa -Qb Several Charges? Ea Eb Ec Ed Ee ETOT ETOT Alan Murray – University of Edinburgh

  18. 1M +1C +2C 1M +2C Worked Example Ftotal 45° F on 1C? Example on board! Alan Murray – University of Edinburgh

  19. Many charges … • Q1, Q2, Q3 …QN • EN = âQN4pe0r2 • E = E1 + E2 + E3 … EN • E = SNEN = SNâQN4pe0r2 • OK for a handful of charges • OK for 1015 electrons/cm3? Alan Murray – University of Edinburgh

  20. Many charges … • For small numbers of charges • Q1(r1), Q2(r2) … QN(rN) is OK to describe a charge Q1 at position r1 etc. • Breaks down as a useful notationfor large N • Instead use r(r) as the density(in Cm-3) of charge at a point r • SNQN becomes ∫r(r)dxdydz = ∫∫∫volr(r)dv Alan Murray – University of Edinburgh

  21. 1mm3 Charge Density : 3D 3D r(r) in C/mm3 1mm3 = r C r(ra) > r(rb) Alan Murray – University of Edinburgh

  22. 1mm2 Charge Density : 2D r(ra) > r(rb) 2D r(r) in C/mm2 1mm2 = r C Alan Murray – University of Edinburgh

  23. 1mm Charge Density : 1D r(ra) > r(rb) 1D r(r) in C/mm 1mm = r C Alan Murray – University of Edinburgh

  24. dE y dEy dEx R r x dq Worked ExampleLong straight “rod” of charge E = (Ex, Ey) Ex = ∫dEx Ey = ∫dEy Alan Murray – University of Edinburgh

  25. dΘ Θ r φ dx rφ Worked ExampleLong straight “rod” of charge r dE dEy rdΘ dEx R r dΘ Θ dq=ρdx y x Alan Murray – University of Edinburgh

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