Electromagnetic Theory IIProblem Set 4Due: 7 February 201115. J, Problem 12.7in SI units. Note that in SI units, the inequalities mentioned in partsb) and c) arep>qBaandp<qBa/2 respectively. Also, in these units, the electromagneticmomentum density is justg=D×B→ǫ0E×Bin empty space.16.Perform a Lorentz boost in thez-direction on the simple circular motion, about theorigin in thexyplane, of a charged particle in a uniform magnetic fieldB=Bˆz.Showthat when expressed in terms of the primed variablesB′,v′, etc., the transformed solutionis precisely that for the general helical motion of a particle in a uniform magnetic field.17. Recall the Lagrangian density for scalar electrodynamicsL=-ǫ04FμνFμν-(∂μ+iQAμ)φ∗(∂μ-iQAμ)φ-U(φ∗φ),Fμν=c(∂μAν-∂νAμ)a) Derive the canonical energy momentum tensor for this Lagrangian defined asTμν=-summationdisplayi∂μψi∂L∂(∂νψi)+ημνL(1)where theψiare the 6 independent fields
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