I am currently studying for O Level and I have been learning about electromagnetism for the past year. The topic has never clicked for me because I've never been taught the true relationship between electricity and magnetism. After looking online, I understand how electromagnetism and magnetism occur on their own (or at least enough to find some closure).

The thing that is still bugging is: why does the magnetic field around a straight current carrying wire 'rotate' a certain direction and not the other? To be specific, I want to understand its direction, not why it's circular. Is it just convention? I know it has something to do with cross-products but not how it applies here.

I know a lot of the topic is beyond my scope but I want to understand why this apparent 'asymmetry' occurs for the time being to rest my curiosity. Thanks for the any help.

  • $\begingroup$ Sorry, I don't understand your question. What do you mean a magnetic field rotates a certain direction? $\endgroup$ – Abhay Hegde Apr 22 '19 at 12:47
  • $\begingroup$ @expikx I mean the right-hand grip rule being used to determine the direction of the field. Say a current is coming towards you, according to the rule, the direction of the magnetic field should be anticlockwise -- but why? Why not clockwise? $\endgroup$ – Typo Apr 22 '19 at 13:56
  • $\begingroup$ It can be clockwise. Anti-clockwise is just a convention similar to assigning positive angle for anti-clockwise rotation. You can define a whole lot of processes with the other convention. Physics stays the same. $\endgroup$ – Abhay Hegde Apr 22 '19 at 13:59

The “right-hand rule” for cross products is just a convention. Physics works fine if you adopt a “left-hand rule” instead. The direction of the magnetic field around a straight wire cannot be directly measured and is dependent on the right-hand convention. All that can be measured is how that field makes charged particles accelerate, and this involves two cross products (the other being in the Lorentz force), so it is independent of the convention.

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  • $\begingroup$ Just asking for some clarification: is the rule then used to just maintain consistency throughout physics? Is there actually nothing important about the direction of the field aside from the fact that it exists? $\endgroup$ – Typo Apr 22 '19 at 14:01
  • $\begingroup$ Yes, the right-hand rule for cross products is just to maintain consistency throughout physics. The tangential nature of the magnetic field around a straight wire is significant. Whether it is considered to loop clockwise or counterclockwise around the wire is not significant and just a convention. You can thank or curse Josiah Gibbs for popularizing vector algebra and vector calculus and introducing the right-hand rule. I would bet that he was right-handed. $\endgroup$ – G. Smith Apr 22 '19 at 18:01
  • $\begingroup$ There are other formalisms for electromagnetism, such as differential forms or Lorentz tensors, in which the magnetic field does not have the asymmetry that bothers you. $\endgroup$ – G. Smith Apr 22 '19 at 18:01

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