Question

4. Rank-2 tensors A charge q moves with a constant velocity tensor rby rHv 2 u. Define the antisymmetric ) where r" is the four velocity of the charge. Further define u (n" =-rH"ru/2. (x-ut)2 1-u2/c2 + y2 + 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 4TC (r2)3/2 Where the

Answer 1

Anses Gue that A chage q mdies pth a Constant velecity To define the antiymetic tenscn YMy yMy here, n is the fous Velocity ef the choge o futhes define y Yuv slas thot TO M-ut let, u - 'x*) è ( y M noxn -, cs Scanned with CamScanner 2e

na-n*M,x°_A,M Y E 1-uye elue =Y (et -ur) let-u Can-l h?- 1k24 let -ux) 22 c-uL cs Scanned with CamScanner

e2-u utJ Therefore (x-ut u'c To show that the slechic field produced bytue yon charge Juen by Enle the Subscript vefers "to the x,3 or2 Go ofE nent 2n the frome of molng charge the field is lectic here cS Scanned with CamScanner

4 transfoRwation yule fo3 tue glectic The field as follos En Ex' НТЕ 3 (и -ин) Y +Z (as the patic le is mouing in X anis Now 2 yo Ex Noo, E3 YEy cs Scanned with CamScanner

EyYy Simihy we an Show the same fos G2 . Hence oh no facto 4/ c n the Enprensio slectic fieldyou Can checle this dimensiohaly aso! Cs Scanned with CamScanner