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Equilibrium of Charges

A charge is said to be in equilibrium, if net force acting on it is zero. A system of charges is said to be in equilibrium if each charge is separately in equilibrium.
 
Types of equilibrium Equilibrium can be divided in following type:
 
Stable equilibrium: After displacing a charged particle from it’s equilibrium position, if it returns back, then it is said to be in stable equilibrium. If U is the potential energy, then in case of stable equilibrium d2U/dx2 is positive, i.e., U is minimum.
 
Unstable equilibrium: After displacing a charged particle from its equilibrium position, if it never returns back then it is said to be in unstable equilibrium and in unstable equilibrium d2U/dx2 is negative, i.e., U is maximum.
 
Neutral equilibrium: After displacing a charged particle from its 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, d2U/dx2 is zero, i.e., U is constant.




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