Eight 8.61-?C charges are arrayed along the y-axis located every 1 cm starting a

Question

Eight 8.61-?C charges are arrayed along the y-axis located every 1 cm starting at y = 0 and extending to y = 7 cm. Find the y-component of the force on the charge at y = 2 cm. Tried using F=(kQQ)/R^2 for each relation. 0->2, 1->2, 2<-3, 2<-4, etc. Set up 7 equations. Each numerator was kQ^2/R^2 where R was 2 for 0->2; 1 for 1->2, 1 for 2<-3, 2 for 2<-4, 3 for 2<-5, etc. I then took the newtons and added them all up, noting that the first 2 are of opposite sign than the other 5. I got .522N, but that is incorrect (so is -.522N).

Explanation / Answer

For charge at y=2, The forces due to 1 and 3 will be same but opposite, so cancels.

Similarly the forces due to 0 and 4 will cancel.

Only, the forces due to 5, 6 and 7 wil act.

F5 = KQQ/(0.05-0.02)2

F6 =  KQQ/(0.06-0.02)2

F7 = KQQ/(0.07-0.02)2

F total = KQQ [(1/0.032) + (1/0.042) + (1/0.052)]

= 1425.2 N

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