electromagnetism and energy causes and effects of static and dynamic electric & magnetic fields...
Post on 21-Dec-2015
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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
ElectrodynamicsGiancoli 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
0
AdEq
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 I0ldB
Changing fields create new fields!
Faraday: Changing magnetic flux induces circulating electric field
Guess what a changing E field induces?
lE ddt
d B
Changing E field creates B field!
Current piles charge onto capacitor
Magnetic field doesn’t stop
Changing
“displacement current”
lB ddt
d E
00
AE dE
Maxwell’s equations
Charge E field Current B field
FaradayChanging B E
AmpereChanging E B
0
AdEq
I0ldB
lE ddt
d B lB d
dt
d E
00
Maxwell eqns electromagnetic waves
Consider waves traveling in the x direction with frequency f=
and wavelength = /k
E(x,t)=E0 sin (kx-t) and
B(x,t)=B0 sin (kx-t)
Do these solve Faraday and Ampere’s laws?
Faraday + Ampere
lE ddt
d B
dx
dB
dt
dE00
dx
dE
dt
dB
lB ddt
d E
00
dx
dB
dt
dE00
dx
dE
dt
dB
Sub in: E=E0 sin (kx-t) and B=B0 sin (kx-t)
00 kEB 0000 BkE
Speed of Maxwellian waves?
Ampere
B0/E0 = 0 v
Faraday
B0/E0 = 1/v
Eliminate B0/E0 and solve for v:
0=xm = xC2 N/m2
Maxwell equations Light
E(x,t)=E0 sin (kx-t) and B(x,t)=B0 sin (kx-t)solve Faraday’s and Ampere’s laws.
Electromagnetic waves in vacuum have speed c and energy/volume = 1/2 0 E2 = B2 /(20 )