emhw18 - Electromagnetic Theory II Problem Set 4 Due 7...

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Electromagnetic Theory II Problem Set 4 Due: 7 February 2011 15. J, Problem 12.7 in SI units . Note that in SI units, the inequalities mentioned in parts b) and c) are p>qBa and p<qBa/ 2 respectively. Also, in these units, the electromagnetic momentum density is just g = D × B ǫ 0 E × B in empty space. 16. Perform a Lorentz boost in the z -direction on the simple circular motion, about the origin in the xy plane, of a charged particle in a uniform magnetic field B = B ˆ z . Show that when expressed in terms of the primed variables B , v , etc., the transformed solution is precisely that for the general helical motion of a particle in a uniform magnetic field. 17. Recall the Lagrangian density for scalar electrodynamics L = - ǫ 0 4 F μν F μν - ( μ + iQA μ ) φ ( μ - iQA μ ) φ - U ( φ φ ) , F μν = c ( μ A ν - ν A μ ) a) Derive the canonical energy momentum tensor for this Lagrangian defined as T μν = - summationdisplay i μ ψ i L ( ν ψ i ) + η μν L (1) where the ψ i are the 6 independent fields
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