Electricity and Magnetism06 MIT公开课 电磁学要点.pdf

Electricity and Magnetism • Reminder – LC circuits / Oscillations – Displacement current – Maxwell’s equations • Today – More on Maxwell’s equations – Electromagnetic waves May 3 2002 LC Circuit L C Spring k Mass m 2 2 2 2 d Q/dt + 1/(LC) Q = 0 d x/dt + k/m x = 0 ω02 = 1/(LC) ω02 = k/m May 3 2002 LC Circuit ½ L I2 L • Total energy U(t) is conserved: C Q(t) ~ cos(ωt) 2 ½ Q /C dQ/dt ~ sin(ωt) UL ~ (dQ/dt)2 ~ sin2 Energy in E-Field UC ~ Q(t)2 ~ cos2 2 2 Oscillation cos (ωt) + sin (ωt) = 1 Energy in B-Field May 3 2002 Electromagnetic Oscillations • In an LC circuit, we see oscillations: Energy in E-Field Energy in B-Field • Q: Can we get oscillations without circuit, i.e. when we have just the fields? • A: Yes! – Electromagnetic Waves May 3 2002 Maxwell’s Equations (almost) Charges are the source of Electric Flux through close surface Changing magnetic field creates an electric field There are no magnetic monopoles Moving charges create magnetic fie