Homework Set # 7 - Due October 21

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      1) Express the Lorenz scalars F^abF_ab,F ^abF_ab, and F^abF_ab in terms of E and B. ( Here F is the dual of F).

2) Is it possible to have an electromagnetic field that appears as a purely electric field in one inertial frame and as a purely magnetic field in some other inertial frame?

      3) What are the criteria imposed on E and B such that there is an inertial frame in which E=0?

      4) Write the continuity equation ∂ρ/∂t+div.J=0 in covariant form in terms of the 4-vector J^µ=(cρ,J).

      5)  Write the tensor transformation for ε_ijkε_mnp . Is it a tensor or a pseudotensor? What is its rank?

      6)  Find out whether V=Ax(BxC)  is a vector or a pseudovector if: a) A, B, and C are all vectors; b) A, B,and C are all pseudovectors; c) A is a vector and B and C are pseudovectors.