The hole in thermodynamics
First I would like to say, sorry for my lengthy absence. School is difficult and boring
I've been pondering electric fields ever since first starting this topic and a few days ago I came across something fascinating.
In my opinion, its ignored by physics because it proves simple laws incorrect and needs a lot of complex math to be proven other wise. That being said, I normally don't ever disagree with math but when it comes to the electric field and work, I just can't help it.
her is a clip from a website. I don't have the image, just imagine a closed loop with a static electric field
Let us now consider the special case where point A is identical with point B. In other words, the case in which we move the charge around a closed loop in the electric field. How much work must we perform in order to achieve this? It is, in fact, possible to prove, using rather high-powered mathematics, that the net work performed when a charge is moved around a closed loop in an electric field generated by fixed charges is zero. However, we do not need to be mathematical geniuses to appreciate that this is a sensible result. Suppose, for the sake of argument, that the net work performed when we take a charge around some closed loop in an electric field is non-zero. In other words, we lose energy every time we take the charge around the loop in one direction, but gain energy every time we take the charge around the loop in the opposite direction. This follows from Eq. (77), because when we switch the direction of circulation around the loop the electric field on the th path segment is unaffected, but, since the charge is moving along the segment in the opposite direction, , and, hence, . Let us choose to move the charge around the loop in the direction in which we gain energy. So, we move the charge once around the loop, and we gain a certain amount of energy in the process. Where does this energy come from? Let us consider the possibilities. Maybe the electric field of the movable charge does negative work on the fixed charges, so that the latter charges lose energy in order to compensate for the energy which we gain? But, the fixed charges cannot move, and so it is impossible to do work on them. Maybe the electric field loses energy in order to compensate for the energy which we gain? (Recall, from the previous section, that there is an energy associated with an electric field which fills space). But, all of the charges (i.e., the fixed charges and the movable charge) are in the same position before and after we take the movable charge around the loop, and so the electric field is the same before and after (since, by Coulomb's law, the electric field only depends on the positions and magnitudes of the charges), and, hence, the energy of the field must be the same before and after. Thus, we have a situation in which we take a charge around a closed loop in an electric field, and gain energy in the process, but nothing loses energy. In other words, the energy appears out of ``thin air,'' which clearly violates the first law of thermodynamics. The only way in which we can avoid this absurd conclusion is if we adopt the following rule:
The work done in taking a charge around a closed loop in an electric field generated by fixed charges is zero.
Hopefully that wasn't to long of a read. anyway, a static field can force and charged particle around a loop continually without performing work or using energy. Net work is zero because it would violate thermodynamics otherwise. Obviously, something is happening for nothing which isn't supposed to happen. According to thermodynamics no work is being done so if you were to harness this movement and create electricity, thermodynamics would not recognize it. Thats my opinion, and its really something cool to think about.
