Transcript E or B? It Depends on Your Perspective

E or B? It Depends on Your Perspective
E or B? It Depends on Your Perspective
Whether a field is seen as “electric” or “magnetic” depends
on the motion of the reference frame relative to the sources of
the field.
E or B? It Depends on Your Perspective
The Galilean field transformation equations are
where V is the velocity of frame S' relative to frame S and
where the fields are measured at the same point in space by
experimenters at rest in each reference frame.
NOTE: These equations are only valid if V << c.
Ampère’s law
Whenever total current Ithrough
passes through an area bounded
by a closed curve, the line
integral of the magnetic field
around the curve is
The figure illustrates the
geometry of Ampère’s law. In
this case, Ithrough = I1 − I2 .
The Displacement Current
The electric flux due to a constant electric field E
perpendicular to a surface area A is
The displacement current is defined as
Maxwell modified Ampère’s law to read
Maxwell’s Equations
Electromagnetic Waves
Maxwell, using his equations of the electromagnetic field,
was the first to understand that light is an oscillation of the
electromagnetic field. Maxwell was able to predict that
• Electromagnetic waves can exist at any frequency,
not just at the frequencies of visible light. This
prediction was the harbinger of radio waves.
• All electromagnetic waves travel in a vacuum with
the same speed, a speed that we now call the speed
of light.
Properties of Electromagnetic Waves
Any electromagnetic wave must satisfy four basic
conditions:
1. The fields E and B and are perpendicular to the direction
of propagation vem.Thus an electromagnetic wave is a
transverse wave.
2. E and B are perpendicular to each other in a manner such
that E × B is in the direction of vem.
3. The wave travels in vacuum at speed vem = c
4. E = cB at any point on the wave.
Properties of Electromagnetic Waves
The energy flow of an electromagnetic wave is described
by the Poynting vector defined as
The magnitude of the Poynting vector is
The intensity of an electromagnetic wave whose electric
field amplitude is E0 is
Radiation Pressure
It’s interesting to consider the force of an electromagnetic
wave exerted on an object per unit area, which is called the
radiation pressure prad. The radiation pressure on an object
that absorbs all the light is
where I is the intensity of the light wave. The subscript on
prad is important in this context to distinguish the radiation
pressure from the momentum p.
Malus’s Law
Suppose a polarized light wave of intensity I0 approaches a
polarizing filter. θ is the angle between the incident plane of
polarization and the polarizer axis. The transmitted intensity
is given by Malus’s Law:
If the light incident on a polarizing filter is unpolarized, the
transmitted intensity is
In other words, a polarizing filter passes 50% of unpolarized
light and blocks 50%.