Question

Chapter 21, Problem 019 In the figure particle 1 of charge +q and particle 2 of charge +4q are held at separation L = 8.88 cm on an x axis. If particle 3 of charge q3 is to be located such that the three particles remain in place when released, what must be the (a) x and (b) y coordinates of particle 3 and (c) the ratio q3/q?

Answer 1

(a)

Let's assume that particle 3 is b/w q1 and q2.

Net force acting on particle 3 = 0

Force on q3 due to q1 = Force on q3 due to q2

kq1q3 / x^2 = kq2q3 / (L - x)^2

q / x^2 = 4q / (L - x)^2

take underroot both the sides,

L - x / x = 2

L = 3x

x = 8.88 / 3

x = 2.96 cm

(b)

y coordinates of particle , y = 0

(c)

Net force on particle 1 = 0

Force on q1 due to q2 = Force on q1 due to q3

kq1q2 / L^2 = kq1q3 / x^2

(x / L)^2 = q3 / q2

((L/3) / L)^2 = q3 / 4q

q3 / q = 4 / 9