maxwell2006 - What is there in the handout What Maxwells...

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Souri Banerjee Souri Banerjee What is there in the handout? What is there in the handout? Maxwell’s equations and electromagnet -ic waves Basic equations of electromagnetism, induced magnetic fields & the displacement current, Traveling waves & Maxwell’s equations, (also in differential forms). Energy transport and Poynting vector, radiation pressure. 38.1 –38.3 Exclude: 38.4 38.5 – 38.7 Griffiths: 7.3.2-7.3.4 Griffiths: 8.1.2 Griffiths: 9.2.1
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Souri Banerjee Souri Banerjee Some Comments Some Comments 0 B = r r • No magnetic analog of q 0 E ε ρ = r r • There is no “magnetic” charge from which lines of can emerge or stop B r Q. Where does the come from? B r
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Souri Banerjee Souri Banerjee Appearance of Magnetic Field Appearance of Magnetic Field J B 0 = × r r r μ The answer in Ampere’s law Magnetic fields “appear” in presence of current. Non-vanishing “Curl” Charges are in motion “Magnetostatic” a misnomer? B r
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Souri Banerjee Souri Banerjee Magnetostatics Magnetostatics Again look back at J B 0 = × r r r μ Take the divergence………. L. H. S. = 0 R. H. S. must be 0 0 J . = r r
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Souri Banerjee Souri Banerjee Continuity Equation Continuity Equation t J . = ρ r r Mathematical statement of charge conservation 0 J . = r r 0 t = ∂ρ steady flow of charge Steady Current: “Magnetostatics” Stationary Charge: “Electrostatics”
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Souri Banerjee Souri Banerjee Beyond Magnetostatics Beyond Magnetostatics 0 J . = r r Charge, for instance, flow in wires that form of complete loops J B 0 = × r r r μ Needs correction Loops contain generator or battery but not ……………………………………. .. a charging capacitor
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Souri Banerjee Souri Banerjee Maxwell Maxwell s Contribution: s Contribution: (1831-1879) “Although the ‘del’ notation was not yet invented, it is mainly due to Maxwell, that the importance of the combinations of the derivatives, which we today call Curl and Divergence , first become apparent” t E o o J o B + = × r r r r εμ μ
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Souri Banerjee Souri Banerjee Displacement Current Displacement Current t E o o J o B + = × r r r r εμ μ ) J J ( d 0 r r + = μ t E J 0 d = r r ε Displacement Current
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Souri Banerjee Souri Banerjee Complete Maxwell Complete Maxwell s Equation s Equation 0 E ε ρ = r r 0 B = r r t E o o J o B + = × r r r r εμ μ t B E = × r r r Symmetry Symmetry restored! restored!
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Souri Banerjee Souri Banerjee Notable points Notable points Surface lies in the plane of the boundary Shape of surface does not affect as long as “loop” does not change 2 1 i i s d . B = r r
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Souri Banerjee Souri Banerjee Resolution Resolution The capacitor Charging! Electric field between the plates varying with time i A 1 dt dQ A 1 t E 0 0 εε = =
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Souri Banerjee Souri Banerjee What Else?
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This note was uploaded on 05/14/2010 for the course MATHEMATIC mathe taught by Professor Xyz during the Spring '10 term at Birla Institute of Technology & Science.

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maxwell2006 - What is there in the handout What Maxwells...

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