Work done by electrostatic force. Positive or negative?

[x86]

Homework Statement

A small, positively charged sphere is released from rest and moves directly away from a larger, positively charged sphere. During this process, the electrostatic force:

a) does positive work and increases the kinetic energy of the small sphere
b) does negative work and increases the kinetic energy of the small sphere

Homework Equations

The Attempt at a Solution

What I know:
1. The kinetic energy of the object is increasing. The system is doing work on it. It's transferring energy to the object.

But at the same time the object is losing potential energy. So it's not really gaining energy. The amount of potential energy lost is equal to the amount of kinetic energy gained. Mechanical energy is still the same. But if it were I could say that the work done by the system (electrostatic force) is positive and the work done on the system is negative. (Is that also right?)

So what is the correct answer? I am confused.

I also have a little bit more confusion. What is the system? Is the system the particle in question, or is the system the object doing work on the particle such as the charge exerting an electrostatic force on it?

 

[TSny]

What I know:
1. The kinetic energy of the object is increasing. The system is doing work on it. It's transferring energy to the object.

But at the same time the object is losing potential energy. So it's not really gaining energy. The amount of potential energy lost is equal to the amount of kinetic energy gained. Mechanical energy is still the same. But if it were I could say that the work done by the system (electrostatic force) is positive and the work done on the system is negative. (Is that also right?)

So what is the correct answer? I am confused.

I also have a little bit more confusion. What is the system? Is the system the particle in question, or is the system the object doing work on the particle such as the charge exerting an electrostatic force on it?

Start with your second question.

It is up to you to decide what you want to take as your system. You can take the small sphere alone as the system. Then the electrostatic force acting on the sphere is an "external" force acting on your system. The work done by that external force corresponds to the change in energy of your system. In this case, your system (i.e., the smaller sphere alone) does not have potential energy; it only has kinetic energy.

Or, you could define the system to be both charges. Then the system can have both potential energy and kinetic energy. There are no external forces acting on this system, so no work is done on the system as the small sphere moves. So, the total energy of the system remains constant. As the small sphere gains kinetic energy, the system loses potential energy.

For your first question, you need to decide on the sign of the work done by the electrostatic force acting on the smaller sphere. To answer this, you don't need to worry about how you define your system. Just think about the direction of the electrostatic force in relation to the direction of the displacement of the smaller sphere.

 

[darkxponent]

You don't need to think do much. A simply apptoach will give you better answer.

dW=F.dx, where F is external force.

it is positive when the direction of force and the direction of movement is same, either both F and dx negative or both positive.

Another way to explain this is to use the work energy theorem as you have done. It states that work done on the object/system is equal to change in 'Kinetic Energy' of the object/system. It doesn't say anything about potential energy. But for work under conservative field(gravity,electric) only the sum of potential plus kinetic is const so you can find the work done as negative of change in kinetic energy.

Regarding you question on system. System is all about reference. If you take only the small positive sphere as the system, then it is experiencing an external force and hence work is done on it.