Two point charges are fixed on the y axis: a negative point charge q 1 = -26 ?C

Question

Two point charges are fixed on the y axis: a negative point charge q1 = -26 ?C at y1 = +0.16 m and a positive point charge q2 at y2 = +0.33 m. A third point charge q = +8.9 ?C is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 23 N and points in the +y direction. Determine the magnitude of q2.

Two point charges are fixed on the y axis: a negative point charge q1 = -26 ?C at y1 = +0.16 m and a positive point charge q2 at y2 = +0.33 m. A third point charge q = +8.9 ?C is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 23 N and points in the +y direction. Determine the magnitude of q2.

Explanation / Answer

force on q due to q1 = F1 = k*q*q1/0.16^2 =9*10^9*26*10^-6*8.9*10^-6/0.16^2 = 81.3515625 N (in +y direction)

force on q due to q2 = F2 = k*q*q2/0.33^2

F1+F2 = F

F2 = F-F1 = 23-81.3515625 = -58.3515625 N (negative force means it's in -y direction)

so, q2 is positive as same charge repel each other and force will be downward... that's negative

so,

9*10^9*q2*8.9*10^-6/0.33^2 =58.3515625

q2 = 58.3515625/(9*10^9*8.9*10^-6/0.33^2) =0.0000793318 = 79.33 uC

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