(a) Consider an infinite charged wire with charges e uniformly spread over it with density n. In the wire frame the charge density is p = en and there is no

current. Consider a frame moving with velocity v along the wire. Using charge conservation and Lorentz space contraction, show that the charge density in the new frame is p' = Bp with B = (1-²-1/2 Find the current density j' and verify that the result for p' and j' is consistent with Lorentz transformation. p' = B(p+ =) j j' = B(j + vp) Calculate the current density j', given that v = (last 4 digit of student ID). (b) Using Gauss' and Ampere's laws, find the electric and magnetic fields around the wire of part (a) in both the wire frame and the moving frame. Verify that the result is consistent with the Lorentz transformation. Er = B (Er-B₂) B₁ = B (B₂ -- Er) where the subscripts refer to the radial and azimuth directions, respectively. Calculate the magnetic fields, B', given that v = (last 4 digit of student ID).