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ANSWER TO QUESTION

Moving charges produce magnetic fields. A negative moving charge (i.e., an electron) produces a North Pole which points anticlockwise around a moving current. A positive moving charge (i.e., a proton) produces a North Pole pointing clockwise. Since electricity is the movement of electrons, which are negative, the field produced around a wire has a clockwise North Pole in the direction of conventional current (anticlockwise if using electron flow). We use the Lorentz force to calculate this, and we choose the direction we do because we are looking at a wire, which is the flow of electrons.

So the answer is not "due to convention," as knowing convention is necessary to answering this question, but is not itself an explanation. If conventions were reversed, the question is still "why this way and not the other?"

Lastly, despite the physics background, this question is philosophical in nature. The answer to the "why" of this question, as opposed to what or how has only lead to more questions unanswerable by current physics, thus, perfectly acceptable for philosophical discussion.

ORIGINAL QUESTION

A current carrying wire produces an electromagnetic force. The magnetic aspect of this force is perpendicular to the wire, and the resulting magnetic force field lines point in the clockwise direction - always.

You can verify by holding a compass near a current carrying wire and observe that North will always point clockwise, and something known as the ‘right hand rule’ helps remember this direction.

A way to think of the question I’m tackling is “what is it about the universe that makes this force point clockwise? Or is all we can say about it is that it points clockwise?”

I am trying to understand if this clockwise direction is explained by something further, whether mathematical or in physics for instance. This question has guided me in various paths. One is that I wanted to see if the direction of magnetic force can be derived from the electromagnetic equations (i.e., Maxwell-Heaviside, Lorentz force law, Biot-Savart) - alas, the equations seem to have direction as an axiom. The direction of vectors is a given, and can only be solved when an initial reference is given.

In other words, the only reason we know the force lines point in the clockwise direction around a current carrying wire is because we observed it to be so. This direction is a fundamental law, it’s not derivable through our knowledge of the universe. We also don’t know which physical properties of the universe, nor do we have a theory, to explain why the direction is the way it is. Seemingly, the electromagnetic equations are designed to take this into account as a given.

Is the “right hand rule” for determining the direction of the resulting magnetic force around a current carrying wire the best we got?

I asked this question on the Physics forum. Please read through it first if interested 1

Here is a visual experiment of the phenomenon I’m speaking of. 2

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Static magnetic fields have their characteristic shape because of (described mathematically by) Ampere's Law. Ampere's law is empirical; it was inferred from data, not derived from more fundamental principles.

Ampere's law can be derived from other expressions in mathematical physics, but at the bottom of every derivation there is still data, not math and metaphysics.

Or if you prefer, the metaphysical principle at the bottom of every derivation is that we can gather data and interpret it using math.

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Consider the magnetic field, the vector B, originating from a wire of infinite length with constant current density, the vector j pointing in positive z-direction.

Then the vector B lies in the (x,y)-plane and is positively oriented with respect to the z-axis.

This follows from

  • choosing the direction of the vector j according to the flow of positive charges, a choice by convention,
  • and solving the Maxwell vector equation rot B = (4pi/c) * j, e.g., using cylindrical coordinates (see Fliessbach, Walliser, Exercise 12.3.)

If one changes the direction of the vector j according to the flow of negative charges, then one gets the negative orientation of B with respect to the z-axis.

Hence the OP’s question has no philosophical background, the answer is simply: Due to a convention.

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Change the direction the current is flowing, i.e. switch which terminals of the power source the ends of your wire are attached to.

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  • Haha I appreciate the humour.
    – Teragreg
    Commented Apr 20 at 3:52

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