Question

u = ux. Define the antisymmetric 4. Rank-2 tensors A charge q moves with a constant velocity (ntrn where n is the four velocity of the charge. Further define tensor r by rHV = 2=-rHrv/2. (x-ut)2 1-u2/c2y+ z2 (a) Show that r2 (b) Show that the electric field produced by the charge is given by En/c = subscript n refers to the x, y or z component of E. q 13/2 where the

4. Rank-2 tensors A charge q moves with a constant velocity u - ux. Define the antisymmetric tensor rue by r--(ημχν-ηνΖ), w 4. Rank-2 tensors A charge q moves with a constant velocity u = uˆx. Define the antisymmetric tensor r µν by r µν ≡ 1 c (η µx ν − η νx µ ), where η µ is the four velocity of the charge. Further define r 2 = −r µνrµν/2. (a) Show that r 2 = (x−ut) 2 1−u2/c2 + y 2 + z 2 . (b) Show that the electric field produced by the charge is given by En/c = q 4π r 0n (r 2) 3/2 , where the subscript n refers to the x, y or z component of E.

Answer 1

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