Electromagnetism and Energy

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Electromagnetism and Energy Causes and effects of static and dynamic electric & magnetic fields Maxwell equations yield electromagnetic waves Electromagnetic energy Thermal energy: heating, melting, boiling, Potential energy: electrostatic, gravitational Kinetic energy Bernoulli equation

Electrodynamics Giancoli Ch.21-29 Physics of Astronomy, winter week 6 Star Date HW: finish CO 3.6, magnitudes Overview of EM & Maxwell’s eqns Minilectures Derive EM wave equation and c Next week: write Interim Research Planning Report Boas Ch.4: partial differentiation (1-6) Week 8: Modern physics + CO Ch.5: Interaction of light and matter

Causes and effects of E Gauss: E fields diverge from charges Lorentz: E fields can move charges F = q E

Causes and effects of B Ampere: B fields curl around currents Lorentz: B fields can bend moving charges F = q v x X = IL x B

Changing fields create new fields! Faraday: Changing magnetic flux induces circulating electric field Guess what a changing E field induces?

Changing E field creates B field! Current piles charge onto capacitor Magnetic field doesn’t stop Changing  “displacement current”

Maxwell’s equations

Maxwell eqns  electromagnetic waves Consider waves traveling in the x direction with frequency f= w/2p and wavelength l= 2p/k E(x,t)=E0 sin (kx-wt) and B(x,t)=B0 sin (kx-wt) Do these solve Faraday and Ampere’s laws?

Faraday + Ampere

Sub in: E=E0 sin (kx-wt) and B=B0 sin (kx-wt)

Speed of Maxwellian waves? Faraday B0/E0 = 1/v Ampere B0/E0 = m0 e0 v Eliminate B0/E0 and solve for v: e0 = 8.85 x 10-12 C2 N/m2 m0 = 4 p x 10-7 Tm/A

Maxwell equations  Light E(x,t)=E0 sin (kx-wt) and B(x,t)=B0 sin (kx-wt) solve Faraday’s and Ampere’s laws. Electromagnetic waves in vacuum have speed c and energy/volume = 1/2 e0 E2 = B2 /(2m0 )