# Electrostatic potential question:what does "Slowly" indicate

1. Sep 30, 2015

### gracy

A charge s moved in an electric field of a fixed charge distribution from point A to another point B SLOWLY.The work done by external agent in doing so is 100J.What is the change in potential energy?Now that is not my actual question.I want to ask what does "SLOWLY" indicate?I know to apply the formula below change in Kinetic energy has to be zero
work done (external)=change in potential energy
for that change in velocity should be zero and for that if particle was at rest initially it should be at rest afterwards and if it was moving with certain velocity it should be moving with the same velocity afterwards thus acceleration should be zero.
But why then question does not mention that acceleration is zero?And why does the question say" slowly"?

Last edited: Sep 30, 2015
2. Sep 30, 2015

### Bystander

It's just one of many ways to indicate/say that a process is being done reversibly.

3. Sep 30, 2015

### gracy

why is reversibility needed?

4. Sep 30, 2015

### DocZaius

I do not see why this has to be done slowly. If the following happens, quickly or slowly, the gained potential energy should be 100 J:

1) A charge is at point A in the static electric field and has kinetic energy x.
2) The charge moves from point A to point B in the static electric field while an external force is applied to it such that the work done on it by that external force is 100 J and such that only the electric and external force are acting on it.
3) The charge is at point B in the static electric field and has kinetic energy x.

if $\int_A^B F_{ext}\,ds=100\,J$ then the change in potential energy is 100 J.

Last edited: Sep 30, 2015
5. Sep 30, 2015

### Khashishi

Slowly implies that the radiation due to accelerated charges is negligible. If you try to move the charge quickly or jerkily then you will lose some energy in electromagnetic waves.

6. Sep 30, 2015

### gracy

But my teacher said Slowly " in this case means that there is no change in kinetic energy of the particle.

7. Sep 30, 2015

### nasu

Doc Zaius

Yes, but you know that the KE does not change. This may be possible if the external force equals the electrostatic force at any point or if it varies in such a way to ensure the net work to be zero.

Moving it slowly is just and awkward way to say that the kinetic energy can be neglected (assuming it starts from rest).
These complication are due to the unfortunate idea to define potential energy in terms of some external forces rather than using the standard definition.

8. Sep 30, 2015

### DocZaius

Calling it awkward is an understatement. Why have your students scratch their heads about whether "slowly" is meant to convey that no energy is lost to radiation, or whether "slowly" means that there is no change in kinetic energy? By the way, the latter interpretation is an odd one indeed. You could move the charge "slowly" and still have it gain kinetic energy.

Why not instead just explicitly state that the charge's kinetic energy does not change, and let the student concentrate on the concepts that you mean to have them concentrate on? This isn't directed at you of course, nasu. It's just this reminds me of the frustrations I experienced as a student while encountering completely unnecessary points of confusion.

9. Sep 30, 2015

### nasu

I agree with you. I was just trying to understand the motives of the authors of the problem.
I would not introduce any external force in the definition of PE.