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An example, here what my textbook says:

When charges are released In electric fields charges experience the force causing them to accelerate along electric field vectors. Positive charges accelerate in the direction of the electric field, negative charges move opposites the electric field. While in motion the charges experienced a change in potential known as a potential difference if charges change speed, then work is done on or by the charges.

My understanding is that if the charges slow down, work is done on them. And if they speed up, work is done by them.

(Why it uses "move" instead of "accelerate" for negative charges?)

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Both can happen simultaneously. This happens in binary star systems all the time.

Work done on object A as it moves from position 1 to position 2 is calculated by $$\int_{\vec{r}_{1A}}^{\vec{r}_{2A}} \vec{F}_{total\,on\,A}\cdot\,d\vec{r}$$. That changes the kinetic energy of A. It could be negative which means the kinetic energy decreases. Some might say that energy flowed out, but that's just different language for "negative work was done on A."

Work done by A on another object B would look at the force (vector) that acts on B due only to A's interaction with B. Integrate that force over the distance that B moves. That work done on B can be positive (increasing KE$_B$) or negative (decreasing KE$_B$).

In your textbook quote, at the end it says: then work is done **on** or **by** the charges. and stops. This doesn't make any sense. It could be "and" vs. "or."

You say: My understanding is that if the charges slow down, work is done on them. And if they speed up, work is done by them.

That is not correct. Negative work on the charge will make a charge slow down. Positive work on the charge will make the charge move faster. Whether a charge does work on something else depends on how the other object moves in response to the force from the charge. And the amount of work is not a reference-frame invariant. If you do the calculations in a different reference frame, the numbers all change.

You ask: (Why it uses "move" instead of "accelerate" for negative charges?) That's not an important distinction worth nit-picking. The context implies that the negative charge is also accelerating.

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  • $\begingroup$ So my textbook is wrong, because there is nothing a charge can exert a force on? $\endgroup$ – most venerable sir Jul 28 '15 at 15:23
  • $\begingroup$ Charges exert forces on other charges via an electric field. $\endgroup$ – Bill N Jul 28 '15 at 15:44
  • $\begingroup$ So you are basically saying "on and by" just indicated the direction of force? If force is exerted on an object by an agent, then work is also done on the object by that agent? $\endgroup$ – most venerable sir Jul 28 '15 at 17:56
  • $\begingroup$ Yes, that's what I said. $\endgroup$ – Bill N Jul 28 '15 at 18:23
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Fundamentally you just need to know which direction energy flows. If energy flows from object (or system) A to object (system) B, object A is doing work on object B which is the same as saying object B is being worked on by object A.

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