Electric Potential enegy and Work

[umdnjmed]

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I read through a few threads on this topic but i'm still confused. Can someone please explain to me when positive or negative work is done on a charge in an electric field.

Consider the following scenario for example; a positive point charge creates an electric field and a negative charge is introduced into the field.This is what i think;
As the negative charge is attracted towards the point charge, it loses potential energy. Therefore, negative work is being done on the charge (but positive work is being done by the charge). Is that correct?

 

[hiaips]

This is what i think;
As the negative charge is attracted towards the point charge, it loses potential energy.

Correct.

Therefore, negative work is being done on the charge (but positive work is being done by the charge). Is that correct?

Not really. Let's look at a concrete example. Support that you have a fixed positive charge located at the origin, and you release a negative charge some distance away. All other forces are negligible.

The potential energy (U) does decrease. However, since the kinetic energy (K) increases at the same time, the electrostatic force actually does positive work on the charge. Another way to see that the work is positive: Because the force is in the same direction as the particle's motion, the angle between them is 0. Since work is the dot product of force and distance, it must be a positive quantity.

Don't forget: The basic equation for work is the dot product of force and distance. Potential energy has nothing to do with this definition.

 

[umdnjmed]

since the kinetic energy (K) increases at the same time, the electrostatic force actually does positive work on the charge.

Is the increase in kinetic energy due to a conversion from potential energy to KE? If it is, wouldn't the work be zero? If is isn't, my next guess would be that the increase in KE is due to the electrostatic force acting on the charge. In the latter scenario, how would the loss of PE be accounted for; would some PE be converted to heat or would the increase in KE of the charge be due to both the electrostatic force acting on it and PE conversion?

Don't forget: The basic equation for work is the dot product of force and distance. Potential energy has nothing to do with this definition.

Thinking of work in terms of the dot product of force and displacement makes perfect sense and does give the correct sign for work. However, isn't energy defined as the ability to do work? It is this definition which led me to conclude that since the charge in the example i gave had a higher potential energy initially, it must have had an "greater ability to do work." Therefore by decreasing its potential energy, its ability to do work must have been put to use by doing work on the surroundings (negative work).

 

[hiaips]

Is the increase in kinetic energy due to a conversion from potential energy to KE? If it is, wouldn't the work be zero? If is isn't, my next guess would be that the increase in KE is due to the electrostatic force acting on the charge. In the latter scenario, how would the loss of PE be accounted for; would some PE be converted to heat or would the increase in KE of the charge be due to both the electrostatic force acting on it and PE conversion?

This is a tricky concept, umdnjmed. You're conflating work with conservation of energy. The total mechanical energy of your system (consisting of both particles) is conserved. You are correct in that energy is merely converted from one form to another.

However, that doesn't mean that work cannot be done on a particle in that system. To quote the work-energy theorem: The change in kinetic energy of an object is equal to the net work of all forces acting upon it.