HW01-Solutions(1) - Physics 201 Homework Solutions 01...

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Physics 201 Homework Solutions 01 CHAPTER 21: Electric Charge & Field 21[6, 8, 13, 17, 27, 42, 56*, 63, 100, 88] *Problems are Optional 1 Problems 21–5 Coulomb’s Law 3 6 9 1mC 10 C, 1 C 10 C, 1nC 10 C . µ = = = - - 6. Since the magnitude of the force is inversely proportional to the square of the separation distance, 2 1 F r , if the distance is multiplied by a factor of 1/8, the force will be multiplied by a factor of 64. ( ) 2 0 64 64 3.2 10 N 2.0 N F F = = × = 8. Use the charge per electron and the mass per electron. ( ) ( ) 6 14 14 19 31 14 16 1 electron 46 10 C 2.871 10 2.9 10 electrons 1.602 10 C 9.109 10 kg 2.871 10 e 2.6 10 kg 1 e × = × × × × × = × 13. The forces on each charge lie along a line connecting the charges. Let the variable d represent the length of a side of the triangle. Since the triangle is equilateral, each angle is 60 o . First calculate the magnitude of each individual force. ( ) ( )( ) ( ) ( ) ( )( ) ( ) 6 6 9 2 2 1 2 12 2 2 6 6 9 2 2 1 3 13 2 2 7.0 10 C 8.0 10 C 8.988 10 N m C 1.20m 0.3495N 7.0 10 C 6.0 10 C 8.988 10 N m C 1.20m 0.2622 N Q Q F k d Q Q F k d × × = = × = × × = = × = ( ) ( )( ) ( ) 6 6 9 2 2 2 3 23 32 2 2 8.0 10 C 6.0 10 C 8.988 10 N m C 0.2996 N 1.20m Q Q F k F d × × = = × = = Now calculate the net force on each charge and the direction of that net force, using components. ( ) ( ) ( ) ( ) o o 2 1 12 13 o o 1 1 12 13 1 1 2 2 1 1 1 1 1 1 2 1 0.3495N cos60 0.2622 N cos60 4.365 10 N 0.3495N sin60 0.2622 N sin60 5.297 10 N 5.297 10 N 0.53N tan tan 265 4.365 10 N x x x y y y y x y x F F F F F F F F F F F θ = + = + = × = + = = × × = + = = = = ° × 1 Q 2 Q 3 Q 12 F d 13 F d d 32 F 31 F 21 F 23 F
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