# Is the following thought experiment about two charges correct?

Let's say I put a charge at a point in space for a long enough time. During this time interval it has set up the electric field in the space.

Then I put another charge in the space. Since the electric field of the first charge has been set up, the second charge "feels" the electric force immediately.

But for the second charge, since its electric field needs some time to reach the first charge, the first charge will "feel" the electric force after a short period.

I think it is weird that their electric force cannot act on each other at the same time. Is it correct or not?

• They will both feel the exact same force at the exact same time. This is Newton's third law. The first charge cannot pull/push in the other without being pulled/pushed itself. – Steeven Feb 18 '15 at 7:34

The second charge would have to be completely shielded, i.e. no induced charge should exist. If this is true, then the answer is yes.

It's not weird when you think about light in the universe. We see the light of galaxies and stars that existed billions of years ago (say, more than 5 Gyr). However, even if they would still exist today, the light of our sun has only traveled through space for 4.5 billion years and it would not yet have reached the distant galaxy.

(I put today in italic, since this is not a very precise notion. What I mean is, that if it was created 6 Gyr $(1 \text{Gyr}=10^9 \text{years})$ ago, it lived for at least 6 Gyr. I hope this is somewhat clearer.)

• But isn't it contradict to the Newton's third law? – hklel Feb 18 '15 at 7:55
• @AlexLing: No. As Surgical Commander correctly states, the information, that something has happend (the sun has disappeared or e 'new' charge has entered our universe) spreads out not instantaneausly, but at the speed of light. – Clever Feb 18 '15 at 14:24

Your question is essentially: at what speed do the fields associated with point charges propagate or respond to changes in the charge distribution. A famous version of this question exists for Newtonian gravity: if the Sun disappeared suddenly, would Earth's orbit immediately change or would there be some delay?

The answer is that it would take the time it takes light to travel the distance between the Earth and Sun for news of the Sun's disappearance to reach Earth. Roughly 8 minutes after the Sun disappeared, the sky would darken suddenly and the orbit would completely change, because both gravitational waves and electromagnetic radiation travel at the speed of light. There is no instantaneous propagation of information of any sort.

The same is happening in your question. If I could sit in another galaxy and oscillate electrons around and you could pick up the signal immediately, then that would be weird and would also violate the known principles of relativity.