# Work by External Force on an electric field

1. Jul 19, 2014

### skepticwulf

I was trying to solve this problem yesterday and I was not able to. I looked it up its solution but my mind is not still clear about it.
"The work done by an external force to move a -6,5C charge from point A to B is 15J. If the charge was started from the rest and had 4.86J of kinetic energy when it reached point B, what must be the potential difference between A and B?"
Solution says "By the work-energy theorem, the total work done, by the external force and the electric field together, is the change in kinetic energy". The rest is just solving the math.
Why I don't understand is this external work, what is it exactly? is this a force that literally TAKES that negative charge and PUT it in point B?? I just can't visualize it. Has this external force PUSHED the negative charge from somewhere to point B so that the charge gained potential energy? I assume this negative charged was moved AWAY from the positive charge so that it can gain potential energy? Am I correct? Then what has exactly this external force done?? How is it that we need to ADD two works to get the kinetic energy?
I'm so confused.
By the way, I'm not posting my homework here, I'm not a student, I'm just trying to understand the concept of electric potential.

Last edited: Jul 19, 2014
2. Jul 26, 2014

### crossfire234

Honestly, saying the charge was moved is just a convention for problem solving. They try to mechanically drive into you the concepts by providing an ideal situation. In reality you cannot imagine moving a single charge, but in theory it helps you learn about the effects of potential energy and electric fields.

Imagine the world as it isn't and I take a charge with my fingers and displace it from A to B in an electric field. The charge would go from positive to negative as you said so that it would gain potential energy. Obviously, the charge will have kinetic energy from me moving it because it's not going to get over there with zero velocity. I am using my breakfast to control my fingers to move the charge which causes me to do work on the system. The work done by potential energy is negative since it runs against your path.

Now with that said we can clear up the math:

$$W_{tot}= \Delta E_k = W_{me} + W_{field}$$

The work done by the field is negative so it goes to:

$$W_{tot} = \Delta E_k = W_{me} -qV$$

And then algebra kills it from there! I hope my explanation is sound and I'm sorry that you're entering a world of purely imaginary situations to help train your real world intuition. Slightly frustrating it is.

I hope this helps!

3. Jul 27, 2014

### crossfire234

P.S. Except for Chaos. Chaos is pretty awesome.

4. Jul 27, 2014

### Staff: Mentor

This is very much similar to moving a mass from point A to point B in a gravitational field, where you are asked to determine the change in gravitational potential energy.

Chet

5. Jul 29, 2014

### Philip Wood

It always seems perverse to me that textbooks define the potential of A relative to B as the work done per unit test charge by an external force on a test charge going from B to A, rather than the work done per unit charge by the field itself on a test charge going from A to B. The definitions are entirely equivalent, but I think bringing in an external force is an unnecessary complication.

6. Jul 29, 2014

### Staff: Mentor

Hi Philip

As you said, potatoes-potahtoes. Personally, the external force version works better for me.

Chet

7. Jul 30, 2014

### Philip Wood

So we don't have to call the whole thing orff?

8. Jul 30, 2014

### Staff: Mentor

Ha!!! Good one. Loved it.

Chet