In the figure particles 1 and 2 of charge q 1 = q 2 = +35.24 In the figure parti

Question

In the figure particles 1 and 2 of charge q1 = q2 = +35.24

In the figure particles 1 and 2 of charge q1 = q2 = +35.24 times 10-19 C are on a y axis at distance d = 17.9 cm from the origin. Particle 3 of charge q3 = +54.46 times 10-19 C is moved gradually along the x axis from x = 0 to x = +5.56 m. At what values of x (in cm) will the magnitude of the electrostatic force on the third particle from the other two particles be (a) minimum and (b) maximum? What are the (c) minimum and (d) maximum magnitudes?

Explanation / Answer

Obviously only Fx matters since the Fys cancel.
Equally obviously, the minimum is at x = 0 where F = 0.
Solving for the maximum:
F = K/r^2, where K is kq1q2.
Fx = F*(x/r) = Kx/r^3.
Fx is proportional to x/r^3 = x / (x^2+y^2)^1.5.
My handy derivative finder (ref.) says the derivative of that function, dFx/dx = (y^2-2x^2)/(x^2+y^2)^(5/2).
Setting the denominator to zero, the maximum should occur when x^2/y^2 = 0.5, or x/y =

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