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We have defined the electric field to easily calculate the force exerted by a system of charges on another charge. What happens to the Electic field if the test charge is removed? Does it still exist or does it vanish? Is there a way to find out and prove its existence in the absence of test charges?

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  • $\begingroup$ Well there is no need for a charge to feel the effects of the Electromagnetic potential (leading to the Electromagnetic field), a proof of this is the Aharonov - Bohm effect $\endgroup$
    – Kregnach
    Aug 7, 2022 at 7:33
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    $\begingroup$ @Kregnach Actually, you do need a charge for the Aharanov-Bohm effect, what you don't need is a magnetic field, that is, a change in the vector potential. But the vector potential only has an effect on charged objects. $\endgroup$
    – Photon
    Aug 7, 2022 at 8:12
  • $\begingroup$ Okay, you are right, to feel te effect there is a need for a test particle, but I think the questioner asked about the source, and the source (In case of the AB effect) doesn't have to be a charged particle. In itself asking whether a field is there or not doesn't make sense, unless you interact with it. $\endgroup$
    – Kregnach
    Aug 7, 2022 at 8:35
  • $\begingroup$ @Kregnach so what u r saying is that if there is no test charge for an interaction, then it is useless to define a field... $\endgroup$ Aug 7, 2022 at 9:11
  • $\begingroup$ If a tree falls and no one is around to hear it… $\endgroup$
    – Gilbert
    Aug 7, 2022 at 10:34

2 Answers 2

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The energy stored in an electric field changes the gravitational field of the charged object. This is only significant in extreme cases like a Reissner-Nordström black hole, but it is a real effect and can in principle be measured.

So you do not need a charged test particle to show that the electric field exists. You can simply measure the gravitational deflection of an uncharged test particle passing the charged object, even a massless test particle like a light ray, and you can measure the strength of the electric field.

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  • $\begingroup$ If your living room has no one in it and no-one is observing it through the window, does it still exist? or does it go into existence, the moment you or someone else loos on it or enters it? You are Sur of its existence since every time you look it is there, So ever time a charge "looks" for the field it is there, So what ist the difference? $\endgroup$
    – trula
    Aug 7, 2022 at 13:13
  • $\begingroup$ @trula are you asking me? Shouldn't this be a comment to the question rather than my answer? $\endgroup$ Aug 7, 2022 at 14:12
  • $\begingroup$ John, you are right, of cause it should be a comment to the question, sorry, I put it in the wrong place. $\endgroup$
    – trula
    Aug 7, 2022 at 15:24
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If you wiggle your original charge, it will emit electromagnetic waves and will experience a radiation reaction force resisting its motion. The energy that goes into the electromagnetic waves has to come from the particle's motion. So you can determine that the energy is still going somewhere, because if you only look at the particle it would appear as if energy was not being conserved.

If you wiggle the charge fast enough, then you can also see the light it emits. Of course, it's arguable that your eyes detect it because of its action on the 'test charge' in the rod/cone receptors in your eyes. So I'm not sure if that counts. An absence of test charges implies an absence of observers, which makes telling anything difficult.

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