In the figure below, particles 1 and 2 of charge q1 = q2 = +3.20 10-19 C are on
ID: 1917321 • Letter: I
Question
In the figure below, particles 1 and 2 of charge q1 = q2 = +3.20 10-19 C are on a y axis at distance d = 15.0 cm from the origin. Particle 3 of charge q3 = +8.00 10-19 C is moved gradually along the x axis from x = 0 to x = +5.0 m. At what values of x 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? (a) position of minimum force m (b) position of maximum force m (c) magnitude of minimum force N (d) magnitude of maximum force NExplanation / Answer
similar model.. 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 = ±sqrt(0.5) or x = 22.6274 cm. At that point F = 8.648276E-27 N. I'm going to run a few cases to confirm this. EDIT: Confirmed it's a maximum.