Question

A negative point charge ` -2q` and a positive charge `q` are fixed ar a distance `l` apart. Where should a postive test charge `Q` be placed on the line connecting the charge for it to be in equlibrium ? What is the nature of the equilibrium with respect to longitudinal motions ?

Answer 1

Correct Answer - ` a = /(a + sqrt 2)`, the equilibrium will be stable .
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`vec F_C = vec F_(CA) + vec F_(CB) =0 rArr F_(CA) = F_(CB)`
`K ( 2 q. Q)/ (( l + x)^2) = ( K.qQ)/x^2`
` x= ( sqrt q)/( sqrt 2q - sqrt q) l = ( sqrt 1)/( sqrt 2-1) l= ( sqrt 2 + 1) l`
Equilibrium will be stable .