Rank-2 tensors a charge q moves with a constant velocity u - ux. define the antisymmetric tensor rue by 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.