Tensors and Relativity: Assignment 4

Hints 4

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  • (1) This derivation is very similar to the one for the conservation of energy equation in section 4.1.2, except this time we are considering the flow of particles rather than energy into the cube.

     

  • (2) The components of the energy momentum tensor tex2html_wrap_inline342 in a general frame (say the lab) are given by

    equation331

    where the tex2html_wrap_inline344 matrices take you from the MCRF to the lab frame.

    The rest of the problem is just filling in the algebra in section 4.1 of the lecture notes.

     

  • (3) Again, this is just filling in the algebra in section 4.2 of the lecture notes.

     

  • (4) This is how you start the this problem. The components of the four- current vector are given by tex2html_wrap_inline346 . We can therefore write the four- force as

    equation336

    Substituting for tex2html_wrap_inline348 from Maxwell's equations gives

    equation338

    The problem now is to manipulate the above into the required form. Remember a bottle of wine rests on this one!!

     

  • (5) This question is worth bonus marks.