Download notes - Purdue Physics

NOTES
Maxwell’s Equations ( incomplete so far)
Gauss’s law
Gauss’ law for magnetism
Faraday’s law
Ampere’s law
Parallel-Plate Capacitor Revisited
-Q
Q
B=0 ? Not
experimentally!
For surface S1, Is = I,
but for surface S2, Is = 0
Wait, LHS is the same
(because C is the same)!
??
You could make this work if a fictitious
current Id is added to Is in such a way that
Id is zero for S1 but is equal to I for S2.
will work.
Displacement Current
James Clerk Maxwell proposed that a changing electric field
induces a magnetic field, in analogy to Faraday’s law: where a
changing magnetic field induces an electric field.
Ampere’s law is revised to become Ampere-Maxwell law
where
is the displacement current.
MAXWELL’S EQUATIONS “COMPLETED”
Basis for Electromagnetic Waves!
The equations are often written in slightly different
(and more convenient) forms when dielectric and/or
magnetic materials are present.
MAXWELLS EQUATIONS
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish
theoretical physicist] His most prominent achievement was formulating a set of
equations that united previously unrelated observations, experiments, and equations
of electricity, magnetism, and optics into a consistent theory. His theory of classical
electromagnetism demonstrates that electricity, magnetism and light are all
manifestations of the same phenomenon, namely the electromagnetic field.
Maxwell's achievements concerning electromagnetism have been called the
"second great unification in physics” after the first one realized by Isaac
Newton.
Maxwell demonstrated that electric and magnetic fields travel through space in the
form of waves at the speed of light in 1865, with the publication of A Dynamical
Theory of the Electromagnetic Field. Maxwell proposed that light was in fact
undulations in the same medium that is the cause of electric and magnetic
phenomena. The unification of light and electrical phenomena led to the prediction
of the existence of radio waves.
TRANSVERSE ELECTROMAGNET WAVE
T E M wave
NOTES
7B-20 TRANSVERSE ELECTROMAGNETIC WAVE
Notation for a TEM wave traveling in the + x direction
( Change + to – for traveling in the – x drection )
Ey = Em sin 2π ( x/λ - t/T )
Bz = Bm sin 2π ( x/λ – t/T )
T=1/f, ω = 2πf
k = 2π/λ
2π/λ measures x the longitudinal extension
2π/T = 2πf measures t the time
ELECTOMAGNETIC WAVE FARADAY INDUCTION PART
Electromagnetic Waves From Faraday’s Law
c
TRANSVERSE ELECTROMAGNETIC WAVE
AMPERE LAW PART
Electromagnetic Waves From Ampère’s Law
Electric Dipole Radiation
Electromagnetic Wave Propagation in Free Space
So, again we have a traveling electromagnetic wave
speed of light
in vacuum
Ampere’s Law
Faraday’s Law
Wave Equation
Speed of light in vacuum is
currently defined rather than
measured (thus defining meter and
also the vacuum permittivity).
NOTES
Plane Electromagnetic Waves
where
c
•  Transverse wave
•  Plane wave (points of
given phase form a plane)
x
•  Linearly polarized (fixed
plane contains E)
Energy Density of Electromagnetic Waves
•  Electromagnetic waves contain energy. We know already
expressions for the energy density stored in E and B fields:
EM wave
•  So Total energy density is
Energy Propagation in Electromagnetic Waves
Energy flux density equals
Energy transmitted through unit time per unit area
•  Intensity I = Average energy flux density (W/m2)
Define Poynting vector
  Direction is that of wave propagation
  average magnitude is the intensity
Radiation Pressure
Electromagnetic waves carry momentum as well as energy.
In terms of total energy of a wave U, the momentum is U/c.
During a time interval Δt , the energy flux through
area A is ΔU =IA Δ t .
  If radiation is totally absorbed:
momentum imparted
radiation pressure EXERTED
  If radiation is totally reflected: x2
Maxwell’s Rainbow
Light is an
Electromagnetic
Wave
NOTES
Physics 241 - Extra QUIZ 3
An electromagnetic wave is traveling in +x direction and the
electric field at a particular point on the x-axis points in the
+z direction at a certain instant in time. At this same point
and instant, what is the direction of the magnetic field?
a) -z
b) -x
c) -y
d) +y
e) None of the above
z
E
y
x The direction of travel
is that of E x B.
Physics 241 – Extra QUIZ 3
An electromagnetic wave is traveling through a particular
point in space where the direction of the electric field is
along the +z direction and that of the magnetic field is along
the +y direction at a certain instant in time. Which direction
is this wave traveling?
a) +x
b) -x
z
E
y c) -y
d) -z
e) None of the above
B
x
The direction of travel
is that of E x B.