HW3
1
PHYS 506 HW3 2 December 2015 Q.1 Consider the Lagrangian density for the electromagnetic field given as L = - 1 8π ∂ μ A ν ∂ μ A ν - 1 c J μ A μ a. Compute the Euler-Lagrange equations of motion for this Lagrangian density. What assumption do you have to make so that the result gives the Maxwell’s equations in its covariant form. b. Compare this Lagrangian density with the one we have discussed in the class (see L em in the cover page) and show that under the assumption determined in part a., and show that they differ only by a 4-divergence. Q.2 Solve problem 12.6 of Jackson ”Classical Electrodynamics” 3rd Edition . Q.3 Solve problem 12.16 of Jackson ”Classical Electrodynamics” 3rd Edition . Q.4 Consider that K 0 frame is in motion with respect to the K frame with velocity v = v ˆ i. Determine the energy density, energy flux density, and the components of the stress tensor in the K -frame in terms of those in the K 0 -frame. Due: 15 December 2015 1 of 1
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electromagnetic theory homework 3
Transcript of HW3
PHYS 506 HW3 2 December 2015
Q.1 Consider the Lagrangian density for the electromagnetic field given as
L = − 1
8π∂µAν∂
µAν − 1
cJµA
µ
a. Compute the Euler-Lagrange equations of motion for this Lagrangian density. What assumption doyou have to make so that the result gives the Maxwell’s equations in its covariant form.
b. Compare this Lagrangian density with the one we have discussed in the class (see Lem in the coverpage) and show that under the assumption determined in part a., and show that they differ only by a4-divergence.
Q.2 Solve problem 12.6 of Jackson ”Classical Electrodynamics” 3rd Edition .
Q.3 Solve problem 12.16 of Jackson ”Classical Electrodynamics” 3rd Edition .
Q.4 Consider that K ′ frame is in motion with respect to the K frame with velocity v = vi. Determinethe energy density, energy flux density, and the components of the stress tensor in the K -frame in termsof those in the K ′-frame.
Due: 15 December 2015 1 of 1
