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)

the electric force of two charges seperated by a distance d is given by

F = Kq1q2/d^2 -------------(1)

if the charge q3 is placed on x axis due to this the net force acting on all particles are zero.(since three particles are same in places)

(a) the net force acting on q2:

therefore F12 = F32

Kq1q2/L^2 = kq2q3/(x-L)^2

? q3/q1 = (L-x)^2/L^2

= ( 8.88 - 2.96)^2 / 8.88^2

= 0.444