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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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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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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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