Solution_Phys351_Test1_2006

# Solution_Phys351_Test1_2006 - Dr Gangopadhyaya Test I...

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Dr. Gangopadhyaya Test I Physics 351 February 20, 2006 To receive full credit you must show your work in a neat, organized and a legible form. First five problems are worth 14 points each and the last problem is worth 30 points. Einstein summation convention assumed NO NAME ON THIS PAGE Eijk = ei . (ej x ek) Eijk Eimn = (jjm(jkn - (jjn(jkm (.4 X B)i = EijkAjBk I ~ p(r') dT' 41TEO IT - f'1 I 1 p(r') (r - r') , dT 41TEO If'- f'13 1. 14 Pts. Using E-symbol, show that .4. (B x C) = (.4x B) . c. A [email protected] c) = ~Ai. (i)(c), = Ai € ijK "BjCIe. :. (Et:ij At Bj) (Ie. (X ~ 8)" C" 1- ... :: \" 'J( i ) . c. (.4. B) = AiBi Electrostatic potential: V(f') - Electric field: E(r) - - - 2. 14 Pts. Three adjacent sides of a rectangular parallelopiped are 2, 3, and 4 units long respectively. Determine the angle between two body diagonals d~ and d-; that ~ connect points (0,0,0) to (2,3,4) and (2,0..4) to (0,3,0) respectively. ,. " " t_" " " 1\+3)+&t1<., d,,:: \.-'2,t +~j-~)(.) \d, \ :: ~ ".. q -tIt. = ~"I J \a) \ : ~ ..... eo S&" ~,,~). :: Dl,d.., \\ -=- 2Cf 9: U;' (-~) ~ ~ -to Ct 1-1" ~, .... d, : " .' -£t+'t -\ b 2.q l1.IO,A) ~,~ )0) '! x

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3. 14 Pts. Explain the difference, if any, between (\7 . .4) iJ and (A. \7) iJ.
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