Two small spheres, each carrying a net positive charge, are separated by 0.400 m

Question

Two small spheres, each carrying a net positive charge, are separated by 0.400 m. You have been asked to perform measurements that will allow you to determine the charge on each sphere. You set up a coordinate system with one sphere (charge q1) at the origin and the other sphere (charge q2) at x = +0.400 m. Available to you are a third sphere with net charge q3 = 3.00×106 C and an apparatus that can accurately measure the location of this sphere and the net force on it. First you place the third sphere on the x-axis at x = 0.200 m; you measure the net force on it to be 6.50 N in the +x-direction. Then you move the third sphere to x = +0.600 m and measure the net force on it now to be 3.50 N in the +x-direction.

Part A) Calculate q1.

Part B) Calculate q2.

Please and Thank You.

Explanation / Answer

  -------------------Q1---------q3----------Q2---------q3-------

F1 = kQ1q3/0,2^2 -kQ2q3/0.2^2 = 6.5

F2 = kQ1q3/0.6^2 - kQ2q3/0.2^2=3.5

F-F2= kQ1q3/0.04 - KQ1q3/0.36 = 3.0

Q1 = 3.0/kq3/(25-25/9) = 5x10^-6

9*10^9*5*3x10^-12*25-6.5= kQ2q3/0.2^2

=3.375-6.5

kQ2q3/0.2^2 = -3.125

Q2 = -3.125*0.04/(9x10^9*3x10^-6)

=-4.63 x10^-6 C

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