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Recently I learnt about conventional current as well as electron flow, and although electron flow is in the opposite direction to conventional current, we still use conventional current because it makes little difference to our calculations.

Yet when we determine the direction of a magnetic field using the right hand grip rule, we use the direction of current flow. If we are given the direction of conventional current, then isn't the direction of the magnetic field suppose to be in the other direction, because in reality the current is the flow of electrons which is opposite to conventional current.

I think there is something wrong with my logic. What is actually going on here?

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    $\begingroup$ The flow isn't necessarily electrons. $\endgroup$
    – John Doty
    Commented Jun 25, 2022 at 22:44
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    $\begingroup$ Our convention for the direction of the magnetic field is just as arbitrary as the direction of the current flow. We have created our model of electromagnetic phenomena in a way that accurately predicts the behavior of the world around us. Arguing about whether the direction of the magnetic field is "actually" opposite to our definition is pointless. $\endgroup$
    – The Photon
    Commented Jun 25, 2022 at 23:08

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The magnetic field is determined by the conventional current, regardless of the sign of the charge carriers.

It is important to understand that the conventional current is the current. In metals the charge carriers are negative electrons but in semiconductors they can be positive holes, and in electrolytes they can be positive and negative ions at the same time. Similarly with plasmas where both positive and negative charge carriers exist.

Personally, I find the “conventional” in “conventional current” to be distracting and unnecessary. It is just current. The current density is defined as $\vec j =\rho \vec v$ so if the charge density $\rho$ is negative then $\vec j$ simply points in the opposite direction as $\vec v$.

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  • $\begingroup$ If conventional current is the actual current then what is electron flow? $\endgroup$
    – Quin Gardiner Bax
    Commented Jun 25, 2022 at 23:34
  • $\begingroup$ @DominicTorreto The actual current is the motion of charge, regardless of what the charge is composed of. If the charge is positive, the current is in the same direction as its motion. If the charge is negative, the current flows in the opposite direction. $\endgroup$
    – John Doty
    Commented Jun 25, 2022 at 23:43
  • $\begingroup$ @DominicTorreto for classical electromagnetism the electron flow is largely irrelevant. The only place it matters in classical electromagnetism is in the Hall effect. Classical electromagnetism was developed before electrons were discovered and so electrons are not necessary for understanding classical electromagnetism $\endgroup$
    – Dale
    Commented Jun 26, 2022 at 0:22
  • $\begingroup$ @Dale I tend to think of vacuum tubes as classical. And I have an old book on vacuum tube electronics that eccentrically defines current flow as electron flow. Thus, it has the "left hand rule" for magnetic fields! $\endgroup$
    – John Doty
    Commented Jun 26, 2022 at 0:43
  • $\begingroup$ @JohnDoty I could see it either way. The electron was discovered in 1897, and the cathode ray tube was invented around 1890. So you don’t need electrons for cathode ray tubes. But vacuum tubes were invented in 1904. So I am not sure how they understood them back then. But regardless of the history, they could treat a cathode ray as a continuous charge distribution $\endgroup$
    – Dale
    Commented Jun 26, 2022 at 3:22

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