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

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Unformatted text preview: 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 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 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 ∂...
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This note was uploaded on 01/08/2012 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.

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