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In studying the world, physicists found that, in order to completely understand what today we call "Electromagnetism", it was necessary to do three things: find an equation which describes the electric field under all circumstances, find an equation which describes the magnetic field under all circumstances, and find an equation which establishes the way these fields act upon matter.

To achieve this, they did three things:

1. Invented the concepts of divergence and curl.

2. Invented Helmholtz's Theorem, which shows that knowing the divergence and curl of a field, you can find the aforementioned equations which completely describe the field.

3. Found the divergence and curl of electric and magnetic fields.

My two questions are:

Isn't this way of describing things rather arbitrary? I mean, the concepts of divergence and curl were kind of taken out of the blue. It's sort of as if physicists said: "let's invent these two properties of fields, calculate them for electric and magnetic fields, and describe these fields using these concepts we just made up."

1.

2.

I'm trying to understand what is the line of thought which led from empirical experiments and data towards these seemingly arbitrary concepts.

To achieve this, they did three things:

1. Invented the concepts of divergence and curl.

2. Invented Helmholtz's Theorem, which shows that knowing the divergence and curl of a field, you can find the aforementioned equations which completely describe the field.

3. Found the divergence and curl of electric and magnetic fields.

My two questions are:

Isn't this way of describing things rather arbitrary? I mean, the concepts of divergence and curl were kind of taken out of the blue. It's sort of as if physicists said: "let's invent these two properties of fields, calculate them for electric and magnetic fields, and describe these fields using these concepts we just made up."

1.

*Is it possible to describe the electric and magnetic fields in different ways, which employ completely different concepts?*2.

*Where can I refer to in order to understand the historical development of the concepts of divergence and curl?*I'm trying to understand what is the line of thought which led from empirical experiments and data towards these seemingly arbitrary concepts.

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