Q: Synchronized clocks are stationed at regular intervals, a million km apart
Synchronized clocks are stationed at regular intervals, a million km apart, along a straight line. When the clock next to you reads 12 noon: (a) What time do you see on the 90th clock down the line? (...
See AnswerQ: Compute the line integral of v = 6 xˆ + yz2
Compute the line integral of v = 6 xˆ + yz2 yˆ + (3y + z) zˆ along the triangular path shown in Fig. 1.49. Check your answer using Stokes’ theorem. [...
See AnswerQ: Prove that the symmetry (or antisymmetry) of a tensor is
Prove that the symmetry (or antisymmetry) of a tensor is preserved by Lorentz transformation (that is: if tμν is symmetric, show that t¯μν is also symmetric, and likewise for antisymmetric).
See AnswerQ: Recall that a covariant 4-vector is obtained from a contravariant
Recall that a covariant 4-vector is obtained from a contravariant one by changing the sign of the zeroth component. The same goes for tensors: When you “lower an indexâ€&#...
See AnswerQ: A straight wire along the z axis carries a charge density λ
A straight wire along the z axis carries a charge density λ traveling in the +z direction at speed v. Construct the field tensor and the dual tensor at the point (x , 0, 0).
See AnswerQ: Obtain the continuity equation (Eq. 12.126) directly
Obtain the continuity equation (Eq. 12.126) directly from Maxwell’s equations (Eq. 12.127).
See AnswerQ: Show that the second equation in Eq. 12.127 can
Show that the second equation in Eq. 12.127 can be expressed in terms of the ï¬eld tensor Fμν as follows:
See AnswerQ: Work out, and interpret physically, the μ=0 component
Work out, and interpret physically, the μ=0 component of the electromagnetic force law, Eq. 12.128.
See AnswerQ: You may have noticed that the four-dimensional gradient operator ∂/∂
You may have noticed that the four-dimensional gradient operator ∂/∂xμ functions like a covariant 4-vector—in fact, it is often written ∂μ, for short. For instance, the continuity equation, ∂μ Jμ=0, h...
See AnswerQ: Show that the potential representation (Eq. 12.133)
Show that the potential representation (Eq. 12.133) automatically satisfies ∂Gμν /∂ xν = 0. [Suggestion: Use Prob. 12.54.]
See Answer
