Fields and sources in different inertial frames 10pt] a) write down the lorentz transformation (a : k - k') for an arbitrary four-vector v using tensor notation (i. e. a is represented by the matrix what is the transformation rule for v? we will now consider a filamentary straight current wire, infinitely long and infinitesimally thin at rest and oriented along the z-axis. let x' be the density of line charge and i' the current in the frame k', in which the wire is at rest. we denote the current with the direction of flux by i i' b) write down the formula for the lorentz transformation for the current j' and the charge density p, expressing the charge density p and current j in a second inertial frame k in terms of j' and p' [hint: it is easiest to work with the four-vector j and then deduce the desired transfor- mation laws. c) find now the current i and line charge density a in the frame in which the wire moves at the velocity v vz. d) show that one can always find a lorentz transformation to a frame where either the magnetic field or the electric field vanish for the former case, find the remaining linear charge density which gives rise to the re- maining electric field, while in the latter case find the remaining current density which gives rise to the remaining magnetic field. can one find a frame of reference in which both the magnetic and electric field vanish at the same time?