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The Galilean Transformations
Introduction to Physics II
Class 20, November 18, 2009
What part of
Today, Ch. 35
• Relating Electric and
Magnetic Fields
• Maxwell’s Equations
• Electromagnetic Waves
Consider two reference frames S and S'. The coordinate
axes in S are x, y, z and those in S' are x', y', z'. Reference
frame S' moves with velocity v relative to S along the xaxis. Equivalently, S moves with velocity −v relative to S'.
The Galilean transformations of position are:
The Galilean transformations of velocity are:
don’t you understand?
E or B? It Depends on Your Perspective
E or B? It Depends on Your Perspective
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.
E or B? It Depends on Your Perspective
Which diagram shows the fields in frame S´?
Recall the cross-product, first studied in Chapter 12,
Ampère’s law
The Displacement Current
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 electric flux due to a constant electric field E
perpendicular to a surface area A is
The displacement current is defined as
In 1864 Maxwell modified Ampère’s law to read:
The figure illustrates the
geometry of Ampère’s law. In
this case, Ithrough = I1 − I2 .
The electric field in four identical capacitors is
shown as a function of time. Rank in order, from
largest to smallest, the magnetic field strength at
the outer edge of the capacitor at time T.
Ba = Bb > Bc = Bd
Bd > Bc > Ba = Bb
Ba > Bb > Bc > Bd
Ba = Ba > Bc > Bd
Bc > Ba > Bd > Bb
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.