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The Galilean Transformations PHY132H1F 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, PHY131: 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. A. B. C. D. E. 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.