what is mean by "charge in an electrostatic equilibrium" ??

[Aladin]

In my text book the definition of the potential difference is that
"The workdone on a unit positive charge carrying it from one point to the other kepping the charge in electrostatic equilibrium"
In my text book electrostatic mean uniform velocity.I am confused!!
why we keep the charge in electrostatic equilibrium? What is the fact that this term is used?
thanks

[Defennder]

Electrostatic equilibrium simply means that no net force is acting on the charged particle, and it doesn't accelerate, ie it's a charge fixed in space. Suppose instead the assumption of electrostatic equilibrium is not given, when a unit positive charge is brought from anywhere in the direction of the reference charge, the reference charge will experience a force, either attractive or repulsive due to the unit positive charge. This means that it would no longer be in electrostatic equilibrium and will be repeled. The idea of potential difference assumes that we can take a test charge and calculate the work done while keeping the conditions the same.

[Doc Al]

In my text book the definition of the potential difference is that
"The workdone on a unit positive charge carrying it from one point to the other kepping the charge in electrostatic equilibrium"
In my text book electrostatic mean uniform velocity.I am confused!!
why we keep the charge in electrostatic equilibrium? What is the fact that this term is used?

What they are getting at is that they want to find the work done against the electrostatic force. So they only want you to exert just enough external force to balance out the electrostatic force. If you don't specify such a restriction, the work done could be arbitrarily large: you could always exert more force than needed, giving the charge extra energy in the process.

An example with gravity: How much work is done in lifting a mass a distance h? If you exert just enough force to balance out gravity, then the work done is mgh. That's the work done "against gravity", but you can always do more.