Definition : A charge is said to be in equilibrium, if total force performing on it is zero. A operation of charges is said to be in equilibrium if each charge is separately is equilibrium.

Type of equilibrium: Equilibrium can be spited in given kind:

(i) Stable equilibrium: After displacing a charged particle from it's equilibrium point, if it goes back then it is called in stable equilibrium. If U is the potential power then in case of stable equilibrium d²U/dx² is positive i.e., U is minimum.

(ii) Unstable equilibrium: After displacing a charged particle from it's equilibrium point, if it never goes back then it is called in unstable equilibrium and in unstable equilibrium d²U/dx² is negative i.e., U is maximum.

(iii) Neutral equilibrium: After displacing a charged particle fro it's equilibrium position if it neither comes back, nor moves away but remains in the position in which it was kept it is said to be in neutral equilibrium and in neutral equilibrium is d²U/dx² zero i.e., U is constant

Different cases of equilibrium of charge:

Case I: Suppose three similar charge Q₁, q and Q₂ are placed along a straight line as shown below

                  Charge q will be in equilibrium if F1 = F2

                  i.e.,Q₁/Q₂ = (x₁/x₂)² ; This is the condition of equilibrium of charge q. After following the guidelines we can say that charge q is in stable equilibrium and this system is not in equilibrium

Case II:      Two similar charge Q₁ and Q₂ are placed along a straight line at a distance x from each other and a third dissimilar charge q is placed in between them as shown below

Charge q will be in equilibrium if F1 = F2

i.e., Q₁/Q₂ = (x₁/x₂)²          

Case III:     Two dissimilar charge Q₁ and Q₂ are placed along a straight line at a distance x from each other, a third charge q should be placed out side the line joining Q₁ and Q₂ for it to experience zero net force.

(Let | Q₂ | < | Q₁ |)

Short Trick: For it's equilibrium. Charge q lies on the side of charge which is smallest in magnitude and d = x/√(Q₁/Q₂-1)

Equilibrium of suspended charge in an electric field

(i) Freely suspended charged particle: To free a charged a particle freely in air under the influence of electric field its downward weight should be balanced by upward electric force for example if a positive charge is suspended freely in an electric field as shown then

In equilibrium QE = mg => E = mg/Q 

(ii) Charged particle suspended by a mass less insulated string: Consider a charged particle of mass m, having charge Q is suspended in an electric field as shown under the influence of electric field. It turned through an angle and comes in equilibrium.

(iii)       Equilibrium of suspended point charge system: Suppose two small balls having charge +Q on each are suspended by two strings of equal size l. Then for equilibrium position as shown in figure:

(iv) Equilibrium of suspended point charge system in a liquid: In the previous discussion if point charge system is taken into a liquid of density r such that q remain same then

In equilibrium F_e^′ = T′sinθ    

and   (mg-Vρg) = T′cosθ  

If s is the density of material of ball then

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