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they leave it ∫ B• dA = 0 Magnetic Monopole
q༇ Paul Dirac argued that the existence of magnetic
monopole may explain the observed quantization of
electric charges.
q༇ Magnetic monopole has not been detected.!
q༇ “ Although there have been tantalizing events
recorded, in particular the event recorded by
Blas Cabrera on the night of February 14, 1982 (thus,
sometimes referred to as the "Valentine's Day
Monopole"), there has never been reproducible
evidence for the existence of magnetic monopoles.“
 Wikipedia Review: (3) Faraday’s Law
q༇ The emf induced in a “circuit” is proportional to the
time rate of change of magnetic flux through the
“circuit” or closed path. dΦB
ε=−
dt
q༇ Since q༇ Then ε= ∫ ∫ nominal
direction of E • dℓ ε B θ dΦ B
E • dℓ = −
dt ΦB = €
€ A ∫ B• dA Review: (4) Ampere’s Law
q༇ A magnetic field is produced by an electric current is
given by the Ampere’s Law ∫ B • dℓ = µ I
0 € q༇ A changing electric field will
also produce a magnetic field
Finally; dΦE
∫ B • dℓ = µ0I + ε0µ0 dt
ΦE = ∫ E • dA Maxwell Equations ∫ q
E • dA =
ε0 à༎Gauss’s Law/ Coulomb’s Law ∫ B• dA = 0 à༎Gauss’s Law of Magnetism,
no magnetic charge dΦB
∫ E • dℓ = − dt à༎Faraday’s Law dΦE
∫ B • dℓ = µ0I + ε0µ0 dt à༎Ampere Maxwell Law Also, Lorentz force Law à༎ F = qE + q v × B These are the foundations of the electromagnetism EM Fields in Space
q༇ Maxwell equations when there is no charge and current: ∫ E • dA = 0 dΦB
∫ E • dℓ = − dt ∫ B • dA = 0 differential forms:
(single polarization)
€
E
B z y x ∂E y ∂Bz
=−
€∂t
∂x ∂2Ey
∂x 2 = µ0ε 0 ∂2Ey
∂t 2 dΦ E
∫ B • dℓ = ε0µ0 dt
∂E y
∂Bz
= − µ0ε 0
∂x
∂t 2 2 ∂ Bz
∂ Bz
= µ0ε 0 2
2
∂x
∂t Figure 346 p1036 Maxwell’s Equations and EM Waves
q༇ Maxwell equations when there is no charge and current: ∫ E • dA = 0 dΦB
∫ E • dℓ = − dt ∫ B • dA = 0 differential forms:
(single polarization)
€
E
B z y x ∂E y ∂Bz
=−
€∂t
∂x ∂2Ey
∂x 2 = µ0ε 0 ∂2Ey
∂t 2 dΦ E
∫ B • dℓ = ε0µ0 dt
∂E y
∂Bz
= − µ0ε 0
∂x
∂t 2 2 ∂ Bz
∂ Bz
= µ0ε 0 2
2
∂x
∂t Linear Wave Equation
q༇ Linear wave equation
certain
physical quantity 2 q༇ Sinusoidal wave
f: frequency 2 ∂y 1∂y
=2 2
2
∂x
v ∂t 2π
y = A sin(
x − 2πft + φ )
λ
A:Amplitude Wave speed φ:Phase λ:wavelength v=λf
k=2π/λ ω=2πf General wave: superposition of sinusoidal waves Electromagnetic Waves
q༇ EM wave equations:
2 ∂ Ey
∂x 2 2 = µ0ε 0 ∂ Ey
∂t 2 ∂ 2 Bz
∂ 2 Bz
= µ0ε 0 2
2
∂x
∂t E
B y
c z
q༇ Plane wave solutions:
E= Emaxcos(kxωt+φ)
B= Bmaxcos(kxωt+φ)
q༇ Properties:
§༊ No medium is necessary.
same φ,
§༊ E and B are normal to each other
set to be 0
§༊ E and B are in phase
§༊ Direction of wave is normal to both E and B
(EM waves are transverse waves)
§༊ Speed of EM wave: c = 1 = 2.9972 × 108 m / s
µ0ε 0
§༊ E/B = Emax/Bmax=c
§༊ Transverse wave: two polarizations possible x The EM Wave
E
B y
c z Two polarizations possible (showing one) x...
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This note was uploaded on 02/25/2014 for the course PHYSICS 202 taught by Professor Pan during the Fall '11 term at Wisconsin.
 Fall '11
 PAN
 Magnetism

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