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04 - Solutions

# 04 - Solutions - Solutions for Homework 4 8 Use the charge...

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Solutions for Homework 4 8. Use the charge per electron and the mass per electron. ! 46 " 10 ! 6 C ( ) 1 electron ! 1.602 " 10 ! 19 C # \$ % & ( = 2.871 " 10 14 ) 2.9 " 10 14 electrons 2.871 " 10 14 e ! ( ) 9.109 " 10 ! 31 kg 1 e ! # \$ % & ( = 2.6 " 10 ! 16 kg 12. Let the right be the positive direction on the line of charges. Use the fact that like charges repel and unlike charges attract to determine the direction of the forces. In the following expressions, k = 8.988 ! 10 9 N " m 2 C 2 . r F + 75 = ! k 75 μ C ( ) 48 μ C ( ) 0.35m ( ) 2 ˆ i + k 75 μ C ( ) 85 μ C ( ) 0.70m ( ) 2 ˆ i = ! 147.2N ˆ i " ! 150N ˆ i r F + 48 = k 75 μ C ( ) 48 μ C ( ) 0.35m ( ) 2 ˆ i + k 48 μ C ( ) 85 μ C ( ) 0.35m ( ) 2 ˆ i = 563.5N ˆ i " 560N ˆ i r F ! 85 = ! k 85 μ C ( ) 75 μ C ( ) 0.70m ( ) 2 ˆ i ! k 85 μ C ( ) 48 μ C ( ) 0.35m ( ) 2 ˆ i = ! 416.3N ˆ i " ! 420N ˆ i 14. ( a ) If the force is repulsive, both charges must be positive since the total charge is positive. Call the total charge Q . Q 1 + Q 2 = Q F = kQ 1 Q 2 d 2 = kQ 1 Q ! Q 1 ( ) d 2 " Q 1 2 ! QQ 1 + Fd 2 k = 0 Q 1 = Q ± Q 2 ! 4 Fd 2 k 2 = Q ± Q 2 ! 4 Fd 2 k 2 = 1 2 90.0 # 10 ! 6 C ( ) ± 90.0 # 10 ! 6 C ( ) 2 ! 4 12.0N ( ) 1.16m ( ) 2 8.988 # 10 9 N \$ m 2 C 2 ( ) % & ( ) * * * = 60.1 ! 10 " 6 C , 29.9 ! 10 " 6 C ( b ) If the force is attractive, then the charges are of opposite sign. The value used for F must then be negative. Other than that, the solution method is the same as for part ( a ).

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Q 1 + Q 2 = Q F = kQ 1 Q 2 d 2 = kQ 1 Q ! Q 1 ( ) d 2 " Q 1 2 ! QQ 1 + Fd 2 k = 0 Q 1 = Q ± Q 2 ! 4 Fd 2 k 2 = Q ± Q 2 ! 4 Fd 2 k 2 = 1 2 90.0 # 10 ! 6 C ( ) ± 90.0 # 10 ! 6 C ( ) 2 ! 4 ! 12.0N ( ) 1.16m ( ) 2 8.988 # 10 9 N \$ m 2 C 2 ( ) % & ( ) * * * = 106.8 # 10 ! 6 C , ! 16.8 # 10 ! 6 C 50. ( a ) Select a differential element of the arc which makes an angle of ! with the x axis. The length of this element is Rd ! , and the charge on that element is dq = ! Rd " .
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04 - Solutions - Solutions for Homework 4 8 Use the charge...

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