Electrostatic Equilibrium of charged particles
Electrostatic Equilibrium:- In equilibrium net electric force on every charged particle is zero. The equilibrium of a charged particle, under the action of Colombian forces alone can never be stable.
Equilibrium is of three types:-
(a) Stable Equilibrium : A charge is initially in equilibrium position and is displaced by a small distance. If the charge tries to return back to the same equilibrium position then this equilibrium is called position of stable equilibrium.
(b) Unstable Equilibrium : If charge is displaced by a small distance from its equilibrium position and the charge has no tendency to return to the same equilibrium position. Instead it goes away from the equilibrium position.
(b) Neutral Equilibrium : If charge is displaced by a small distance and it is still in equilibrium condition then it is called neutral equilibrium.
Problem Solving strategies:-
(1) Equilibrium of three point charges:-
(ii) Third charge should be of unlike nature as
(2) Equilibrium of symmetric geometrical point charged system:-
Value of Q at centre for which system to be in state of equilibrium:-
Q=[ -q/√3 ]
Q= [ -q(2√2+1)/4 ]
(3) Equilibrium of suspended point charge system:-
T cosθ = mg and T sinθ = Fe = kQ2/x2
⇒ tanθ = [ Fe /mg ] = [kQ2/x2mg ]
If q is small then
tanθ ≅ sinθ = [x/2l] ⇒ x/2l = kQ2/x2mg
⇒ x3 = 2kQ2l/mg
⇒ x = [ Q2l/2πε0mg ]1/3
If whole set up is taken into an artificial satellite (g≅0) :-
then T = Fe = kq2/4l2