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30_Ch 15 College Physics ProblemCH15 Electric Forces and Electric Fields

30_Ch 15 College Physics ProblemCH15 Electric Forces and Electric Fields

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30 CHAPTER 15 15.58 As shown in the sketch, the electric field at any point on the x -axis consists of two parts, one due to each of the charges in the dipole. 2 2 e e k q k q E E E r r + + = = ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 4 e e e e k q k q x a x a ax E k q k q x a x a x a x a x a 2 + = = = + + 2 2 x a >> Thus, if , this gives 4 3 4 4 e e k qa ax E k q x x = 15.59 (a) Consider the free-body diagram for the ball given in the sketch. 0 sin37.0 or sin37.0 x x x qE F T qE T Σ = ° = = ° 0 cos37.0 or y y F qE T mg qE qE Σ = + ° = + and Thus, cot37.0 y x mg ° = ( ) ( ) ( ) 3 2 5 8 1.00 10 kg 9.80 m s cot37.0 5.00 3.00 cot37.0 10 N C 1.09 10 C 10.9 nC y x mg q E E × = = + °
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