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Two particles (free to move) with charge...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`.
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