Figure (a) shows charged particles 1 and 2 that are fixed in place on an x axis.

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 |q_1| = 11e. Particle 3 of charge q_3 = +11e. Particle 3 of charge q_3 = +11e 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 magnitudes of the net electrostatic ofrce on particle 2 due to particles 1 and 3 changes. Figure (b) gives the x component of that net ofrce as a function of the position x of particle 3. The scale of the x axis is set by x_s = 2.20 m. The plot has an asymptote of F_2, net = 0.4615 times sign 10^25 N as x right arrow infinity. As a multiple of e and including the sign, what is the charge q_2 of particle 2?

Explanation / Answer

at x = 2xs the F2,net = 0

F12 = F32

k*q1*q2/r12 = k*q3*q2/r23

q1/x12 = q3/2xs

x12 = 2xs

from the graph at infinity asymptote = 0

F2net = k*q1*q2/r12^2

0.4615*10^-25 = (9*10^9*11*1.6*10^-19*q2)/(2*2.2)^2

q2 = 5.64*10^-17 C

q2 = (5.64*10^-17)/(1.6*10^-19) = 352.5e

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