329fall12hw1sol - D = A B = 3 4 z x y A B 3C = 2 4 12 x y z...

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D = A + B =3ˆ x y z A B +3 C =2ˆ x +4ˆ y + 12ˆ z | A B C | = 2 2 +4 2 + 12 2 = 12 . 81 A +2 B C =(ˆ x y +2ˆ z )+2(2ˆ x ˆ y ˆ z ) x y +3ˆ z )=4ˆ x y z | A + 2B C | = ° 4 2 +( 7) 2 3) 2 =8 . 60 ˆ u = A + 2B C | A + 2B C | = x y z 8 . 6 =0 . 47ˆ x 0 . 81ˆ y 0 . 35ˆ z A · B x y z ) · (2ˆ x ˆ y ˆ z )=1 × 2+( 3) × ( 1) + 2 × ( 1) = 3 B × C =(2ˆ x ˆ y ˆ z ) × x y z )=2ˆ x × x y z ) ˆ y × x y z ) ˆ z × x y z ) =(4ˆ z y ) ( ˆ z x ) y x )= ˆ x y +5ˆ z Q 1 = 12 πε 0 Q 2 = Q 1 / 3= 4 0 P 3 Q 1 Q 2 E 3 = ± 2 i =1 Q i 4 0 | r 3 r i | 2 · r 3 r i | r 3 r i | = 3 | ˆ y | 3 (0 ( ˆ y )) 1 | ˆ y | 3 (0 ˆ y y (V / m) P 4 E 4 = ± 2 i =1 Q i 4 0 | r 4 r i | 2 · r 4 r i | r 4 r i | = 3 | ˆ y z | 3 y z ) 1 |− ˆ y z | 3 ( ˆ y z y z 2 (V / m) P 5 E 5 = ± 2 i =1 Q i 4 0 | r 5 r i | 2 · r 5 r i | r 5 r i | = 3 ˆ x y | 3 ( ˆ x y ) 1 ˆ x ˆ y | 3 ( ˆ x ˆ y ˆ x y 2 (V / m)
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E B v F v F F = q ( E + v × B ) x = E 0= E +(
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329fall12hw1sol - D = A B = 3 4 z x y A B 3C = 2 4 12 x y z...

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