Question

Two particles (free to move) with charges `+q` and `+4q` are a distance L apart. A third charge is placed so that the entire system is in equilibrium.
(a) Find the location, magnitude and sign of the third charge.
(b) Show that the equilibrium is unstable.
A. ` Q= 4/9 q ("negative" ) at l/3`
B. `Q= 4/9 q ("positive" ) at l/3`
C. ` Q= q ("positive" ) at l/3`
D. `Q=q("negative" )at l/3`

Answer 1

Correct Answer - A
For equilibrium of system `Q` must be negative Taking equlibrium at `A`
` K(4q.Q)/x^2 = K (4 Q.Q)/ l^2 rArr sqrt (Q)/(x) = sqrt Q/l`

`x= sqrt Q/q l rArr x = 2/3 l` ltbr Taking equilbrium at `C,K. (4 qQ)/x^2 = (KQ.q)/((l-x)^2)`
`4 (l - x )^2 = x ^2 rArr x/l = 2/ 3` ...... (2)
From (1) and (2) `Q = 4/9 q`.