I know how magnetic flux is mathematically defined, and it clearly has dimensions of kg m^2 A^-1 S^-2, but I've read magnetic flux being described as "number of magnetic field lines passing through an area". Doesn't that imply magnetic flux is a pure number? And if this is incorrect, what would the intuitive definition (as opposed to B.A) for flux be?
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$\begingroup$ it clearly has dimensions of kg A^-1 S^-2 No, it doesn’t. See Wikipedia. $\endgroup$– G. SmithCommented Nov 26, 2020 at 20:49
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$\begingroup$ typo. Sorry about that $\endgroup$– Vulgar MechanickCommented Nov 26, 2020 at 21:22
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$\begingroup$ number of magnetic field lines passing through an area There is a field line passing through each point. This means that the number of field lines through any finite area is infinite. $\endgroup$– G. SmithCommented Nov 26, 2020 at 21:27
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I've read magnetic flux being described as "number of magnetic field lines passing through an area"
That is probably not a very good source to be learning from. This source basically has it backwards. You don’t start with field lines, count them, and get the flux. Instead you start with the flux and then draw field lines such that the number of field lines per area is roughly proportional to the flux. The proportionality is rough since you only draw a finite number of lines.
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$\begingroup$ so you're saying that magnetic flux is proportional, but not equal to the number of field lines? secondly, aren't field line just a diagrammatic way of representing the field, with the concentration showing the relative strengths? $\endgroup$ Commented Nov 27, 2020 at 7:40
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$\begingroup$ Yes. Understanding them helps to draw fields and make quick qualitative assessments $\endgroup$– DaleCommented Nov 27, 2020 at 14:09