Critical Thinking

A frictionless circular track with a diameter of 4.00 m has two spheres of 10.0 kg each anchored very near it. The track is oriented with a diameter along the x-axis. The anchored spheres are just outside the track. One of the anchored spheres is just left of the origin at a distance of $1.00 \times 10^{- 15} \text{m}$ from it, and the other is on the x-axis just right of the track at a distance of $1.00 \times 10^{- 15} \text{m}$ past $\left(4 , 0\right)$. Each sphere carries a charge of $2.00 \times 10^{- 9} \textrm{ }\text{C}$. (Note: The slight distance from the track is so the particles cannot collide, and does not enter into the calculations for three significant figures.) (a) A third sphere has a mass of 10.00 kg and carries a charge of $- 1.00 \times 10^{- 9} \textrm{ }\text{C}$. It is free to move on the track. It is initially placed an equal length from the two anchored spheres at $\left(2.00 , 2.00\right)$. What is the total force on the third sphere? (Be certain to include gravity between the spheres.) (b) Will the third sphere move? (c) Label the first two spheres A and B, and the movable sphere C. Now start sphere C at $\left(1.00 , 2.00\right)$. What are the forces on sphere C? (d) Will sphere C now move? (e) If it does, where will it stop moving and reverse course? If it does not move, you may skip this part. (f) How many equilibrium points are there on the track at which the movable sphere will remain stationary? Where are they?