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I am well aware that a charged particle moving in a magnetic field will experience a force perpendicular to that magnetic field. But why is it that positive and negative particles experience a force in opposite directions?

What exactly determines the direction that a given charge will experience a force? I.e. why does a negative particle experience a force in one direction and not the other?

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  • $\begingroup$ Not sure what you mean: the Lorentz force is $ \vec F = q \vec v \times \vec B$ where q is the charge: if you change the sign of the charge, the force is in the opposite direction. $\endgroup$ – NickD Feb 14 '18 at 20:30
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    $\begingroup$ It is an experimental fact that there are two different types of charges in the universe, identifiable exactly because they empirically experience forces in opposite directions - no more, no less. $\endgroup$ – gented Feb 14 '18 at 20:34
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    $\begingroup$ The comment I made recently on a related question is equally applicable here. If you are willing to accept relativity and electrostatics then you can get magnetostatics for "free", but the starting place is the understanding that science has to be correctly descriptive before any other concerns enter. $\endgroup$ – dmckee♦ Feb 14 '18 at 20:47
  • $\begingroup$ Start by forgetting about positive and negative. Just imagine that you find out that a charge is attracted. You test more charges and suddenly stumble upon one that is repelled. After countless of experiments and searches you have only found these two cases. So you decide to name them something: Why not positive and negative charges, now that it seems like a binary pattern? If we ever in the future find a third version of a reaction pattern, then we might get some issues in finding a new name... But so far we haven't. Why it is like this, is a good question $\endgroup$ – Steeven Feb 14 '18 at 20:55
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The problem with the why in your question is that it will give rise to another why in the explanation to explain why that explanation occurs and so on; giving rise to an infinite number of whys. But to kick things off, I'll try and give an initial explanation:

Charges deflect in a magnetic field dependent upon their charge sign because of:

We can move to a laboratory moving at the same instantaneous velocity as the charge where it now appears stationary. Any magnetic field here cannot affect the charge because it's not moving; leaving only an electric field, if any, that can affect it. This electric field will deflect that the charge in one of two ways depending upon its sign, which will also be seen in one of two ways in the original laboratory where the charge was moving.

Now we're left with another two questions which I can't give an answer to:

  • Why is Lorentz symmetry (the principle of relativity) engrained within physics?
  • Why does an electric field deflect a charge dependent upon its sign?
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Electromagnetism is symmetric with respect to parity. That symmetry is broken by the convention we choose to use for defining the magnetic field vector. Aliens on another planet could define magnetic fields to point in the opposite direction compared to our definition. They would then use a left-handed rule $\textbf{F}=-q\textbf{v}\times\textbf{B}$ rather than our right-handed $\textbf{F}=q\textbf{v}\times\textbf{B}$. If you get in radio contact with these aliens and try to get them to tell you whether their definitions are the same as ours or opposite, you can't tell without some external reference point that tells them which hand you consider right.

What exactly determines the direction that a given charge will experience a force? I.e. why does a negative particle experience a force in one direction and not the other?

why is it that positive and negative particles experience a force in opposite directions?

You can express the rules in ways that don't refer to the magnetic field or its arbitrarily defined flippable direction. For example, parallel current-carrying wires attract each other if the currents are in the same direction. Such rules are independent of which charges you define as positive and which way you define the magnetic field.

When expressed in these ways that avoid the arbitrary conventions, these rules follow from special relativity. The classic presentation at the freshman physics level is in the textbook by Purcell.

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I'm not really sure to have understood your question, however you have to consider the sign of the charge inside the formula: $$\mathbf{F_{Lor}}=q\mathbf{v}\times\mathbf{B}$$ and so if: $$q=|q|$$ $$\mathbf{F_{Lor+}}=|q|(\mathbf{v}\times\mathbf{B})$$ instead if: $$q=-|q|$$ $$\mathbf{F_{Lor-}}=-|q|(\mathbf{v}\times\mathbf{B})$$ How you can see: $$\mathbf{F_{Lor-}}=-\mathbf{F_{Lor+}}$$ The force acting on a postive and on a negative charge are opposite vectors.

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    $\begingroup$ Instead if you are asking why Lorentz force exists, I don't know how to answer. $\endgroup$ – Landau Feb 14 '18 at 20:57
  • $\begingroup$ -1 The asker is already aware that the forces on +ve and -ve particles are in opposite directions. $\endgroup$ – sammy gerbil Feb 14 '18 at 23:09
  • $\begingroup$ Still not able to read the mind of the asker@sammygerbil $\endgroup$ – Landau Feb 15 '18 at 9:36
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I've been told I can't just link to another site so I will try to paraphrase the article I linked to. The magnetic force is perpendicular to the velocity of the particle it is acting on. That causes the direction of the particle to change and travel in a circular motion. https://cnx.org/contents/bZRPyVNP@2/Motion-of-a-Charged-Particle-i

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  • $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$ – Martin Feb 14 '18 at 21:00
  • $\begingroup$ I can see your point about the link changing Martin. Is is ok to paraphrase it and include the link as I did? $\endgroup$ – Mike Molland Feb 14 '18 at 21:58
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    $\begingroup$ -1 This answer is not useful. It does not say anything which is not already in the question. $\endgroup$ – sammy gerbil Feb 14 '18 at 23:07
  • $\begingroup$ It is the only answer that does not just state an equation. It explains why the motion is in circular form. $\endgroup$ – Mike Molland Feb 14 '18 at 23:15
  • $\begingroup$ @MikeMolland That wasn't the question, though. The question was why does it curve the specific direction that it does. $\endgroup$ – Chris♦ Feb 15 '18 at 1:13

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