Two point charges are fixed on the y axis: a negative point charge q1 = -33 ?C a

Question

Two point charges are fixed on the y axis: a negative point charge q1 = -33 ?C at y1 = +0.19 m and a positive point charge q2 at y2 = +0.31 m. A third point charge q = +9.7 ?C is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 27 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 = -33 mu C at y1 = +0.19 m and a positive point charge q2 at y2 = +0.31 m. A third point charge q = +9.7 mu C is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 27 N and points in the +y direction. Determine the magnitude of q2.

Explanation / Answer

First we find the force on q by q1 using Coulomb's Law
F = k*q*q1/r^2 = 9.0x10^9N-m^2/C^2*9.7x10^-6C*33x10^-6C/(0.19^2) = 79.8N and it points up

Now since the resulting force is 27N up the force on q by q2 must point down and have a magnitude of 79.8 - 25. = 52.8N.

Now for the magnitude F = 52.8 = k*q*q2/r^2

so q2 = 52.8N*r^2/(k*q) =52.8*(0.31)^2/(9x10^9*9.7x10^-6) = 1.8x10^-5C = 18

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