Coulomb's Law Word Problem

Question

Figure (a) shows charged particles 1 and 2 that are fixed in place on an x axis. Particle 1 has a charge with a magnitude of |q1| = 22e. Particle 3 of charge q3 = +22e is initially on the x axis near particle 2.Then particle 3 is gradually moved in the positive direction of the x axis. As a result, the magnitude of the net electrostatic force on particle 2 due to particles 1 and 3 changes. Figure (b) gives the x component of that net force as a function of the position x of particle 3. The scale of the x axis is set by Xs= 2.00 m. The plot has an asymptote of F2,net = 1.777 × 10-25 N as x →infinity. As a multiple of e and including the sign, what is the charge q2 of particle 2?

Answer 1

Hello Will,

The information provided in figures (a) and (b) would be need to provide a complete solution of the problem you have presented. I believe I can provide some of the key points of the solution, however. F_2,Net represents the (x-component) of the net force on particle 2. Let F₁₂ and F₃₂ be the x-components of the forces on particle 2 produced by particles 1 and 3, respectively. Thus, F_2,Net = F₁₂ + F₃₂. Regardless of the precise details in the figures, the key observation is that F₃₂ → 0 as x →∞. Therefore, as x→∞, F_2,Net → F₁₂. That is, the asymptotic value of F_2,Net is equal to F₁₂. If you can send diagrams, I could help out with the remainder of the solution. Feel free to schedule a lesson if you need more help.

William