TransWikia.com

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

Physics Asked by Predaking Askboss on July 3, 2021

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 $r$.

One Answer

This does not cause any problems with the conservation of energy. The conservation of energy in EM holds locally and is described by Poynting’s theorem. As the theorem says, if the matter gains energy then the fields lose it and vice versa.

Answered by Dale on July 3, 2021

Add your own answers!

Ask a Question

Get help from others!

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP