43 10 15 112 1493 fj b e 1 z 2 8 xyz a x 4 x 2 z a y

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= -4/3 10 -15 [ 112 ] = -448/3 10 -15 = -149.3 10 -15 = -149.3 fJ (b) E = 1 z 2 (8 xyz a x + 4 x 2 z a y 4 x 2 y a z ) v/m d L = 2 m Q = 6-nc P (2 , 2 , 3) a L = 6/7 a x - 3/7 a y - 2/7 a z d L = a L . d L = 2 m ( 6/7 a x - 3/7 a y - 2/7 a z ) = 2 10 -6 m ( 6/7 a x - 3/7 a y - 2/7 a z ) Q = -QE.d L Q = (-6 10 -9 ) 1 z 2 8 xyz a x + 4 x 2 z a y 4 x 2 y a z .d L = -6 10 -9 2 10 -6 1 z 2 8 xyz a x + 4 x 2 z a y 4 x 2 y a z . 6/7 a x - 3/7 a y - 2/7 a z = -12 10 -15 1 z 2 (8 xyz)(6/7) + ( 4 x 2 z )(-3/7) ( 4 x 2 y)(-2/7) = -12 10 -15 1 z 2 48/7 xyz - 12/7 x 2 z + 8/7 x 2 y Putting values x = 2 , y = -2 and z = 3 = -12 10 -15 1 (3) 2 (48/7) (2)(-2)(3) + (-12/7) (2) 2 (3) + (8/7 )(2) 2 (-2) = -12 10 -15 1 9[ -576/7 - 144/7 - 64/7 ]
Professor Aatif Saeed Preston University Islamabad Page 18 = -4 10 -15 1 3 [-576-144-64] 7 = -4/3 10 -15 [ -112 ] = 448/3 10 -15 = 149.3 10 -15 = 149.3 fJ (c) E = 1 z 2 (8 xyz a x + 4 x 2 z a y 4 x 2 y a z ) v/m d L = 2 m Q = 6-nc P (2 , 2 , 3) a L = 3 /7 a x + 6/7 a y d L = a L . d L = 2 m ( 3 /7 a x + 6/7 a y ) = 2 10 -6 m ( 3 /7 a x + 6/7 a y + ) Q = -QE.d L Q = (-6 10 -9 ) 1 z 2 8 xyz a x + 4 x 2 z a y 4 x 2 y a z .d L = -6 10 -9 2 10 -6 1 z 2 8 xyz a x + 4 x 2 z a y 4 x 2 y a z . 3 /7 a x + 6/7 a y = -12 10 -15 1 z 2 (8 xyz)(3/7) + ( 4 x 2 z )(6/7) = -12 10 -15 1 z 2 24/7 xyz + 24/7 x 2 z Putting values x = 2 , y = -2 and z = 3 = -12 10 -15 1 (3) 2 (24/7) (2)(-2)(3) + (24/7) (2) 2 (3) = -12 10 -15 1 9[ -288/7 + 288/7 ] = -4 10 -15 1 3 [-288+288 ] 7 = -4/3 10 -15 [ 0 ] = 0 J ANSWER D4.2. Calculate the work done in moving a 4-C charge from B (1 , 0 , 0) to A (0 , 2 , 0) along the path y = 2 2 x , z = 0 in the field E = ( a ) 5 a x V/m; ( b ) 5 xa x V/m; ( c ) 5 xa x + 5 ya y V/m. Solution : ( a) Q = 4C A (0 , 2 , 0) B (1 , 0 , 0) Path y = 2- 2x z = 0 E = 5 a x v/m A W = -Q E.d L B A