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Quiz_1_ solution

# Quiz_1_ solution - Solution to Quiz 1 April 9 2010 1 Answer...

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Solution to Quiz 1 April 9, 2010 1. Answer: d. Solution: (By dimension analysis, a., b. and c. can be ruled out first.) Flux ϕ : ϕ = surface E · d A = a 0 dx a 0 dyE z = a 0 dx a 0 dyE 0 y 2 b 2 = aE 0 1 b 2 a 0 y 2 dy = E 0 a 4 3 b 2 . 2. Answer: e. Solution: Denote q 1 = +20 × 10 - 6 C, q 2 = - 10 × 10 - 6 C, q 3 = - 4 × 10 - 6 C. r 1 = (12 ˆ ı + 0 ˆ ȷ ) m, r 2 = (12 ˆ ı + 5 ˆ ȷ ) m, r 3 = (0 ˆ ı + 0 ˆ ȷ ) m. Displacement vector r 13 from q 1 to q 3 : r 13 = r 3 - r 1 = - r 1 = - (12 ˆ ı + 0 ˆ ȷ ) m, Magnitude r 13 = ( - 12) 2 + ( - 0) 2 m = 12 m Unit vector ˆ r 13 from q 1 to q 3 : ˆ r 13 = r 13 r 13 = - ˆ ı, F 13 = k q 1 q 3 r 2 13 ˆ r 13 = ( 9 . 0 × 10 9 N · m 2 /C 2 ) × ( 20 × 10 - 6 C ) × ( - 4 × 10 - 6 C ) (12 m ) 2 ( - ˆ ı ) = ( 5 × 10 - 3 ˆ ı ) N Displacement vector r 23 from q 2 to q 3 : r 23 = r 3 - r 2 = - r 2 = - (12 ˆ ı + 5 ˆ ȷ ) m, Magnitude r 23 = ( - 12) 2 + ( - 5) 2 m = 13 m Unit vector ˆ r 23 from q 2 to q 3 : ˆ r 23 = - ( 12 13 ˆ ı + 5 13 ˆ ȷ ) , 1

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q 1 q 2 E 13 E 23 E x y 0.1m 0.1m 0.1m Figure 1: F 23 = k q 2 q 3 r 2 23 ˆ r 23 = ( 9 . 0 × 10 9 N · m 2 /C 2 ) × ( - 10 × 10 - 6 C ) × ( - 4 × 10 - 6 C ) (13 m ) 2 ( - 12 13 ˆ ı - 5 13 ˆ ȷ ) = ( - 1 . 97 × 10 - 3 ˆ ı - 8 . 19 × 10 - 4 ˆ ȷ ) N F 13 = F 13 + F 23 = ( 5 × 10 - 3 ˆ ı - 1 . 97 × 10 - 3 ˆ ı - 8 . 19 × 10 - 4 ˆ ȷ ) N F = (5 × 10 - 3 - 1 . 97 × 10 - 3 ) 2 + ( - 8 . 19 × 10 - 4 ) 2 N = 3 . 14 × 10 -
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Quiz_1_ solution - Solution to Quiz 1 April 9 2010 1 Answer...

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