Two small charged spheres (S1 and S2) are suspended from a common point P by cords of equal length l, as shown in the figure below, and make small angles, a1 and a2, with the vertical through P. The charge on S1 is Q and the charge on S2 is 2Q (same polarity). The mass of S1 is m1 and the mass of S2 is m2. For this particular problem, the mass of S2 is given as twice that of S1.
Part A - We are asked to find the ratio of the two angles a2/a1.
Part B - Estimate the distance d between the two spheres.
The Attempt at a Solution
I reasoned that each sphere's equilibrium position would be the result of where along the swing arc the tangential components of the graviatational and repulsive electrical force acting on it (Fg_ and Fe_) would cancel each other out. These tangential components are shown above as Fgt1 & Fet1 for S1 and Fgt2 & Fet2 for S2. Note that the magnitude of electrical force acting to repel each sphere is given by Coulomb's Law using Q and 2Q as the charge values and d as the distance between the sphere's centers.
The magnitude of the tangential components of the electrical and gravitational forces acting on S1 and S2 are:
Since the spheres are at rest, Fet1 = -Fgt1 and Fet2 = -Fgt2:
Dividing eq. 3 by eq. 4:
Before I show where I'm stuck for Part B, does eq. 6 answer Part A or have I messed up somewhere?
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