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The question is basically the title, that can two positive or negative electric charges attract each other, there is no constraint on the sizes of the charge.

Can only electrostatic force result in attraction .

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    $\begingroup$ Are you interested in the strong force that holds protons and neutrons together in the atomic nucleus? $\endgroup$
    – The Photon
    Commented Apr 19, 2023 at 15:54
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    $\begingroup$ Cooper pairs are an example of an indirect way. $\endgroup$
    – M.S.
    Commented Apr 19, 2023 at 17:00
  • $\begingroup$ Like charges may approach each other if that repulsion is overtaken by other forces, possibly electro static. Consider ions attracted together. As other mentioned the strong nuclear force does this. Alternatively you can do physics restricted to the surface of a sphere. The more charge you add, the closer the charges get to each other. Move a charge away from its stationary point, some particles in the direction opposite the motion will approach it, right? $\endgroup$
    – R. Romero
    Commented Apr 20, 2023 at 4:53
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    $\begingroup$ Can only electrostatic force result in attraction? Well, gravity is also attractive. $\endgroup$
    – Qmechanic
    Commented Apr 20, 2023 at 6:54
  • $\begingroup$ i only meant that can they attract because of electrostatic force $\endgroup$
    – Curious
    Commented Aug 4, 2023 at 13:34

3 Answers 3

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Two similar (like) electric charges will never attract if only the electrostatic force is considered. However, if some other forces are acting between them and if they are strong enough (stronger than the opposing electrostatic force between the charges), the two similar (like) electric charges will move towards each other. The force may be gravitational force (because of their masses); strong force (because of their colour charge) or any other force.

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  • $\begingroup$ But what if you use logic given by @naturallyInconsistent $\endgroup$
    – Curious
    Commented Apr 19, 2023 at 17:09
  • $\begingroup$ Yes, his/her reasoning is right. However, the way he/she answered seems confusing. I have also conveyed the same idea as him/her. $\endgroup$
    – user355398
    Commented Apr 19, 2023 at 18:35
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Two like charges cannot be attracted electromagnetically. This can be seen easily by looking at the directions of coulomb forces between two positive or negative particles. However, in nature, there are important cases when this electromagnetic repulsion is overcome by a stronger attractive force--namely the binding of nucleons into nuclei.

Consider a $^4$He nucleus: two positive protons and two neutrons bound together in a stable configuration. How can this happen if the protons repel electromagnetically? The answer is through the longer-range form of the strong force that holds nucleons together. At this length scale, the strong force is mediated by pion exchange between nucleons. Therefore, the protons and neutrons are constantly exchanging pions and the resulting attractive force dominates over the electromagnetic repulsion and the nucleus is stable.

Since you don't put limits on the sizes of these charged objects, you could also imagine a system of two large objects with like charges than gravitationally attract each other.

In summary, if two like-charged objects are attracted to each other, there must be another force at play rather than just the electromagnetic.

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    $\begingroup$ One of example suggested by @naturallyInconsistent features the case of a large metallic sphere with a charge Q and a small object with a charge Q close to the surface of a sphere. In this case, the object attracts to its mirror image in the sphere, and this force can easily overcome the repulsion from the sphere center. Note that all the forces here are purely electromagnetic. $\endgroup$
    – E. Anikin
    Commented Apr 19, 2023 at 16:13
  • $\begingroup$ This definitely works for macroscopic objects, thanks for adding. $\endgroup$
    – klippo
    Commented Apr 19, 2023 at 16:21
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    $\begingroup$ And now I am incredibly confused as to why my answer is being downvoted... $\endgroup$ Commented Apr 19, 2023 at 16:47
  • $\begingroup$ @naturallyInconsistent if you wrote your answer a bit more clearly it would be better $\endgroup$
    – Curious
    Commented Apr 19, 2023 at 16:53
  • $\begingroup$ @TejasJohar but I am not supposed to just give you the answer. Not to mention that each of the 4 questions immediately implied that there are cases there that answered your question directly. $\endgroup$ Commented Apr 19, 2023 at 17:01
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Can one of the positive charges be a big metallic sphere?

Can these positive charges be nucleons?

Can these positive charges be incredibly heavy?

Can these positive charges be moving in the same direction very very quickly? Edit: Rob points out why this case is wrong.

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  • $\begingroup$ So you mean that there would be some polarization near the other charge? $\endgroup$
    – Curious
    Commented Apr 19, 2023 at 17:00
  • $\begingroup$ Yes, that is a definite possibility. Your question is just posed to widely that it is unclear what loopholes you would have accepted. $\endgroup$ Commented Apr 19, 2023 at 17:02
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    $\begingroup$ This should be a comment. $\endgroup$
    – d_b
    Commented Apr 19, 2023 at 17:36
  • $\begingroup$ Your fourth example is incorrect. If two charges repel in their rest frame, they repel in all frames. The magnetic attraction becomes equal to the electric repulsion in the limit that you boost to $v=c$. $\endgroup$
    – rob
    Commented Apr 26, 2023 at 9:07
  • $\begingroup$ @Rob Thanks. Edited to say that that case is wrong. $\endgroup$ Commented Apr 26, 2023 at 9:36

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