B When to Use f = -dU/dx with External Energy Sources?

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The discussion revolves around the application of the formula f = -dU/dx in scenarios involving external energy sources. A commenter questions the validity of using this formula when an external energy source, like a battery, is present. The response clarifies that the kinetic energy gained by the slab equals the change in field energy of the capacitor, making the total work done by the battery consistent with the formula. However, there is confusion about the original question and its context, leading to a consensus that addressing it may not be productive. The thread ultimately concludes without further resolution.
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In the above video , at time 3:45 to 3:49 he used the formula ##\frac{-dU}{dx}##
There is a comment which says
How can u use f=- du/dx. In case when there is external source of energy?

And answer given to this comment is as follows

In this case we can do this. As here you can calculate and see that the gain in kinetic energy of slab is exactly same that of the change in field energy of capacitor and sum of the two is the work done by battery so it
will not make any difference.


I don't understand the question as well as answer . Why we can't use ##\frac{-dU}{dX}## when external source of energy is present?
 
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gracy said:
I don't understand the question
You should ask the person who asked the question. We would just be guessing

It is hard enough to answer your own questions to your satisfaction that I do not think that it will be productive for us to try and answer someone else's question to your satisfaction.

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