PHYS 671: Homework IIIdue date: Thursday, October 31st, 2013 at class meeting.Total number of points: 120. You need 100 points for full score (50 points areextra credit).You are welcome to work together. If you partially use work from others (e.g. somethingyou might have found in a book or a journal paper), you should properly credit the author byciting the material used. Be sure to properly write problem/question numbers you are answer-ing.1. The covariant formulation of Maxwell’s equations presents a ”dual” symmetry (Fµν↔Fµν). It is possible to extend this symmetry to the source term of Maxwell’s equations.We assume the existence of a magnetic charge g (not yet experimentally detected as oftoday). [50 pts](a) Write down the modified covariant form of the Maxwell’s equations (field created bythe source jµand kµdue to the motion of a particle with charges q and g, and thecovariant form of the equation of motion (duα/dτ = ...). [10 pts](b) Expand all these covariant equations into the standard four Maxwell’s equations,and the two dynamics equation (dp/dt = ... and dγ/dt = ...). [10 pts](c) Could you briefly comment is there exist a transformation of j0, q, k0, g,−→j ,−→k ,−→E ,and−→B that results in the theory you developed to be invariant by spatial reflection(−→x → −−→x ). [5 pts](d) Write down the E-field produced by the electric charge q located at the origin. Byanalogy write the B-field produced by the charge g located at the distance−→d fromq. [10 pts](e) Compute the Poynting vector induced by the static field generated by the charge qand g. [5 pts](f) Write the form (do not compute the integral) of the angular moment−→J producedby these two charges along the−→d -direction and compare to the product gq. [5 pts](g) (for fun) In the framework of a quantum theory of this system, what is the conditionthe product gq should satisfy? [5 pts]12. Jackson’s 3rd edition, problem 12.6 [30 pts − (a): 15 pts, (b): 15 pts].3. Jackson’s 3rd edition, problem 14.5 [20 pts − (a): 10 pts, (b): 10 pts].4. Jackson’s 3rd edition, problem 14.11 [20 pts − (a): 10 pts, (b): 10