# Isn't Velocity of Electric field a violation of law of conservation of energy?

Let take two positive charges $$q_1$$ and $$q_2$$. There are four points. $$q_1$$ was initially located at (a), and $$q_2$$ was at (d). Distance between (a) to (d) is taken 1 lightsecond. Distance between (b) and (c) is also about 1 lightsecond (but a little less)

(a)...(b)................(c)...(d)

$$q_1$$.................................$$q_2$$

$$q_1$$is moved from (a) to (b) toward $$q_2$$, and in a similar way, $$q_2$$ is moved from (d) to (c) toward $$q_1$$. Let say they both were pushed for half a second. Due to speed of electric field, during the push, $$q_1$$ and $$q_2$$ will not feel any change in position of each other. For the force applied during the time of the push, we assumed that $$q_2$$ was at (d) for $$q_1$$, and for $$q_2$$, $$q_1$$ was at (a). The confusion here is that the energy transferred that $$q_2$$ got (as a signal) would be greater than the energy needed to push $$q_1$$, because for $$q_2$$, $$q_1$$ is moved, and the distance between them is less than the distance that of $$q_1$$ felt during push.

(For Energy given) $$\text{Force on } q_1 = \dfrac{Kq_1q_2}{r^2 }$$

(For energy output) $$\text{Force on } q_2 = \dfrac{Kq_1q_2}{r'^2 }$$

When we think about $$r$$, we found that it would be somewhere between distance of (a) - (d) and (b) - (d), as the electric field of $$q_2$$ will be there the same for 1 second. But for $$r'$$, it is between (a)-(d) and (b) - (c), so $$r>r'$$. Therefore, the force on $$q_2$$ is greater.

Assume that you are $$q_1$$ and are pushed for 1/2 second over a very short distance. You will find that field of $$q_2$$ were the same there for that time period as a result of the velocity of the electric field. So, the $$q_2$$ for $$q_1$$ was at (d) during push. Thus, $$q_1$$'s average distance from $$q_2$$ was somewhere between (a) - (d) and (b) - (d).

However, for $$r'$$ taken for force on $$q_2$$ for receiving signal was different from $$r$$. Here, I am $$q_2$$ and was moved at the same time, but when your changed electric field reached me after 1 second, I was also moved closer. So, for me, you moved closer, and I also moved a little closer to you, which makes my average distance from $$q_1$$ less than $$r$$.

• Hello! It is preferable to use MathJax (LaTeX) to display formulas. You can find a tutorial at MathJax basic tutorial and quick reference. Please edit your question accordingly. Thanks! – Jonas Apr 8 at 21:31
• Yes i repeated a thing few times like showing that r is greater than r' so that one can get why i said that. Describing the whole situation. Ya i didn't know more about equations that's why i tried to use statements – Predaking Askboss Apr 9 at 16:09