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Chapter 12: Q10P (page 518)
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Show that the second equation in Eq. 12.127 can be expressed in terms of the field tensor as follows:
localid="1654746948628"
鈥淚n a certain inertial frame S, the electric field E and the magnetic field B are neither parallel nor perpendicular, at a particular space-time point. Show that in a different inertial system , moving relative to S with velocity v given by
the fieldsare parallel at that point. Is there a frame in which the two are perpendicular?
An ideal magnetic dipole moment m is located at the origin of an inertial system that moves with speed v in the x direction with respect to inertial system S. In the vector potential is
(Eq. 5.85), and the scalar potential is zero.
(a) Find the scalar potential V in S.
(b) In the nonrelativistic limit, show that the scalar potential in S is that of an ideal electric dipole of magnitude
located at .
A Lincoln Continental is twice as long as a VW Beetle, when they are at rest. As the Continental overtakes the VW, going through a speed trap, a (stationary) policeman observes that they both have the same length. The VW is going at half the speed of light. How fast is the Lincoln going? (Leave your answer as a multiple of c.)
Show that the potential representation (Eq. 12.133) automatically satisfies 
[Suggestion: Use Prob. 12.54.]
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