# Question about electric field doing work

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1. Jun 16, 2016

### RoboNerd

1. The problem statement, all variables and given/known data

. The problem statement, all variables and given/known data

If the electric field does negative work on a negative charge as the charge undergoes a displacement from position a to b within an electric field then the electrical potential energy is?

2. Relevant equations
none

3. The attempt at a solution
So I know that W = -deltaU, and thus, if we have a negative coefficient for W, we would get a positive coefficient for deltaU, resulting in positive electrical potential energy.

How could I think this problem through if I completely forgot the equation and just thought conceptually?

2. Jun 16, 2016

### Simon Bridge

Considering they mention the charge, you are probably expected to start with F=qE and W=Fd.

3. Jun 17, 2016

### Stavros Kiri

Is the problem the sign for you to remember? Because W = -ΔU [or ΔU = -W] is in fact by definition of potential energy [or/and potential energy difference], and really an easy one to remember! Then one just needs to pick a point of reference where U = 0, or carry an arbitrariness up to a constant.
So it is better that you don't forget that equation. It is (almost) the only way (+see ahead). It is by definition.

Unless you are looking for the motivation that also helps us justify why exactly we define it that way. And that is nothing else but the Conservation of Energy. [That's how I always remember it, and the sign.] Please pay attention closely to my next post.

Note: The electric potential V is related to the electrical potential energy through V = U/q . Also E = F/q (or F = qE). Finally, the work of a force F is defined roughly as:
W = ∑FΔs (or better W = abF•ds).
(cf. also Simon Bridge's comment above/ for connection ...)

Last edited: Jun 17, 2016
4. Jun 17, 2016

### Stavros Kiri

Here is the interesting part:
Assume there are no external forces. Due to "the change of kinetic energy theorem": W = ΔΕkinetic . Also here W = -ΔU. Thus:

ΔΕkinetic = -ΔU or ΔΕkinetic + ΔU = 0 or Δ(Εkinetic + U) = 0,
or ΔEtot = 0, i.e. conserv. of the total energy, as promised.

Last edited: Jun 17, 2016
5. Jun 17, 2016

### Stavros Kiri

Here is a 3rd version/interpretation of your problem, which for you may in fact be the primary one.
If we know that W<0, then, even without the q<0 assumption (it is irrelevant), we get by conservation of total energy etc.: ΔU = -ΔEkinetic = -W > 0, q.e.d

The same is obtained directly by W = -ΔU ... as you said, but you also say "you are afraid you might forget! ..." ...

6. Jun 19, 2016

### RoboNerd

Thank you for the kind answers. Yes, I understand how the law of conservation of energy works... but I am looking for like a pretend scenario to think of.

For example, if I were to be considering moment of inertia, I would instantly think of a rod spinning at the center being easier to twirl around than a rod at one end. This would give me some intuition to solve problems

How would I be able to "think" or "visualize" electrons and electric fields to get the right answer?

Thanks!

7. Jun 19, 2016

### Stavros Kiri

Electric field lines diagrams perhaps?
Or particularly for potential energy?

8. Jun 20, 2016

### RoboNerd

I do not know. How would I use electric field diagrams or particularly for potential energy?

9. Jun 21, 2016

### Stavros Kiri

Last edited: Jun 21, 2016
10. Jun 22, 2016

### RoboNerd

I know how electric field diagrams work, I just need to figure out how to imagine a sample scenario from which I would derive the right answer.

What i am asking for is sort of like deriving the differential equation for the motion of an object in simple harmonic motion where I know the initial set up and can logically and quickly derive the right answer.

11. Jun 23, 2016

### Stavros Kiri

Then the only thing I can think of is [creating a set-up by] going back to the basics, i.e. Coulomb's law (for electrostatics + the test charge can move), Lorentz force law (for E and B fields and moving charges), + writting down Work and energy equations properly (to properly move to potentials etc.), etc.
That way you can derive almost everything in E&M (including Maxwell's equations - with the help of Special Relativity transformations [and for non-accelerating charges]), but sometimes the math is too much, and that method is problably not an "economic" one, so sometimes we better off remember some things and already existing results, while in other cases, or purely for educational or fundamental foundational purposes, that, I agree, is a good method and motivation (to think that way), because it helps us understand things better. For non complicated situations it is a good idea.

But may be somebody else has more ideas and suggestions. Or perhaps, after this interaction in the discussion, you can come up with better ideas and suggestions.

12. Jun 23, 2016

### RoboNerd

Sorry, special relativity is a bit over my head now. I did not cover Lorentz force law, but I can cover it in the future.

So thus, I am not able to derive the equations yet, as I do not have special relativity knowledge. Maybe later, if and when I cover it.

13. Jun 24, 2016

### Stavros Kiri

That goes may be for the complete E&M theory, which is relatively advanced in math.

But you can still create the set-up that you want (and I think it is in fact a good idea) for Electrostatics [note that the test charge can move] (and similarly for magnetostatics), by going back to the basics, that is the notion of charge, Coulomb's force law etc., and with the use of simple mechanics ideas and some calculus you can derive most equations (besides the definitions of course). For example from Coulomb's law you first find E = F/q , then through the work of the force you get the potential energy and the electric potential etc.
But we have already discussed these basic issues and you seem to be familiar with them. Thus you won't have a problem creating the appropriate set-up for every situation and derive the equations that you want. But keep in mind what the definitions are, in each case, in that process. (For example ΔU = -W is by definition, as already said earlier, while the formula for electric potential (V [or Φ]) of one charge (Q) field: V(r) = K•(Q/r) , is a result (following by the also definition of potential V = U/q and the calculation of mechanical work [and thus of potential energy] for Coulomb's force ... [q is the test charge]).)
So there are many things you can do.

For the complete E&M theory and connection to special relativity, don't worry about it now. In any case, you have to go through the usual presented method first. For example (later) you will learn Maxwell's equations as generalizations of the E&M laws and you will pretty much have to accept and remember them before you even have to worry about the connection to sp. relativity and ways to formally derive them. Historically they also came about first, before and independent of the STR.

Last edited: Jun 24, 2016
14. Jul 10, 2016

### RoboNerd

OK. thanks for the input! I definitely have to keep it in mind.

15. Jul 11, 2016

### Stavros Kiri

Thanks also for the discussion and interaction.

I particularly liked and admired overall your idea and desire to always go back to the foundation and derive everything, instead of just blindly remember the equations, as contained/expressed in:
That is always a more secure, productive and creative way to do physics, than just memorizing and quoting ...

16. Jul 11, 2016

### RoboNerd

Thank you!

Physics should not be memorized. Only understood. Otherwise, it becomes a useless memorization exercise.

17. Jul 11, 2016

### Stavros Kiri

I agree.
(May be some memorization is accompanying and somewhat innevitable, but the priority is I think what you say ...)

Last edited: Jul 11, 2016