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Like we cannot define set, we can not define a point, they all are fundamental notions. Mathematics starts from Set, Euclidian Geometry starts from Point. Here is one attempt to define a point: "A point is a geometrical entity with zero length, zero width, zero height only having a position", But this statement is not what we call DEFINITION because here we are using terms like length, width etc. Now if I ask you what is the definition of length, I think you will use the term "point" to define length, if so, then I must say that you are giving me a circular statement and it can't be a definition. You can also say that a point is a circle with zero radius etc..., but this also is not a definition. I think You can only give statements which express your notion about a point Unless you have more fundamental entity than a point.

In a similar manner, I think Electrodynamics starts from Charge (as for myself, I use Griffiths Introduction to electrodynamics. As far I can remember, he didn't define charge). But here: "What is charge?" I found people claiming the definition of the electric charge. I don't know if there exists more fundamental entity before charge. There they used E-M field to define charge. If so, Then I request to give me the DEFINITION of E-M field completely independent of using the term charge.

DanielC
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sid
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  • Firstly, I suggest not demanding things. Secondly, see this answer: https://physics.stackexchange.com/a/109592/82528 – Omry Oct 10 '17 at 07:23
  • Sorry! I've edited my question, and Thanks for noting my language mistake and giving your concerned COMMENT instead of giving ANSWER, And Thanks for providing the link which I'd already seen but didn't understand and posted my question. – sid Oct 10 '17 at 07:52
  • Possible duplicates: https://physics.stackexchange.com/q/57199/2451 , https://physics.stackexchange.com/q/106605/2451 , https://physics.stackexchange.com/q/109535/2451 and links therein. – Qmechanic Oct 10 '17 at 08:35
  • @Qmechanic: There the answer given by "https://physics.stackexchange.com/users/12813/wonderich" sounds fascinating but I didn't understand it. I'm an under graduate student. Is it possible to give me an independent definition of charge? If You use the word E-M field to define charge, then your definition of E-M field should not involve the term Charge. Is it possible? – sid Oct 10 '17 at 08:55

3 Answers3

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The EM field is the curvature of a U(1) Yang-Mills theory. Charge is the conserved Noether quantity corresponding to same U(1) gauge symmetry.

This probably was not helpful. But for a helpful answer you may have to ask rather than demand.

TimRias
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    @sid The point is, you can give experimental/phenomenological definition, which is not "precise" but easily understandable, or you can give a "satisfying" definition, which requires advanced math.

    To phrase the answer in more clear terms, a field is charged, if it is invariant under rotations of the complex plane. Charge is a number that indexes possible representations of this rotation.

     – Bence Racskó Oct 10 '17 at 08:19
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You can't say anything which will be called definition of charge because it is an intrinsic property of elementary particles like rest mass ,spin,parity etc. We simply say that it is the property due to which a particle produces electric and magnetic fields and experiences electric and magnetic interaction.

Rajendra Pd
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The basal definition of charge comes from experiments done with scraps of cloth and furs alongside bits of amber, glass, etc. The name "electricity" is based on the Greek word for amber, "elektron". It was Ben Franklin who defined negative charge as being the static charge produced on amber when rubbed with cloth (e.g. flannel).

We've bootstrapped quite a bit from there, to the point where the unit of charge is defined in terms of current, oddly enough, though we may be switching to defining charge/current in terms of the charge of the electron.

Point being, this isn't pure math. This is physics. We define things like charge by providing examples, or at least instructions on how to produce examples for yourself.

Sean E. Lake
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  • As far I can remember, Once Galileo said,"Mathematics is the language with which God wrote the Universe." – sid Oct 10 '17 at 08:11
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    That's a nice, beautiful quote, but also completely irrelevant. The philosophy of science has advanced a long way since then. – Sean E. Lake Oct 10 '17 at 08:24
  • I thought this was relevent because I thought we can't step forward without the help of Mathematics – sid Oct 10 '17 at 08:32
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    This is all true, but we can define charge via symmetry groups in QFT, and that, I believe, is the only definition that doesn't eventually reach a circular logic (i.e., defining charge through current makes you ask what is current? Well, a current is defined through charge, so...). – Omry Oct 10 '17 at 12:12