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 CurrentThe 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 WavesMaxwell, 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

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.

Any electromagnetic wave must satisfy four basic conditions:

The energy flow of an electromagnetic wave is described by the Poynting vector defined as

The magnitude of the Poynting vector is

Properties of Electromagnetic Waves

The intensity of an electromagnetic wave whose electric field amplitude is E0 is

Radiation PressureIt’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 LawSuppose 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%.