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We have been studying electromagnetic induction in Physics and when calculating Flux Linkage our teacher insisted the unit is Weber-Turns since it is the flux times the number of turns. I put forward that the turns is a unitless measure since it is just a quantity. It would be like saying, one apple weighs 100g so 10 apples must weight 1 kilogram-apples. That sounds ridiculous.

She agreed with my logic but says the exam board use Weber-Turns so it's probably correct but feel free to check. I am aware that this is not incorrect but I would like to confirm that it is redundant for my own sanity. It is referenced on the internet by both so it's not apparent whether one is more accurate or logical than the other.

Tim Hargreaves
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2 Answers2

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A turn as a unit is indeed dimensionless. But so is radian, and it's still used extensively. Such units are useful as bookkeeping devices, so it's better to use them when appropriate, although technically you could omit them.

As for your example with apples, you're being a bit incorrect. Mass of an apple is 100 grams per apple. So multiplying it by 10 apples gives you 1 kilogram, which is not ridiculous at all.

Ruslan
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  • Following your logic with the apple though: The flux in one coil will be the flux per coil (like grams per apple) and therefore the flux linkage should be measured in Webers [Turns * Flux/Turn]. How can we jump two powers of turns by multiplying by it once? – Tim Hargreaves Feb 25 '17 at 20:28
  • Too late to edit but by flux per coil I meant Weber per turn. Apologies. – Tim Hargreaves Feb 25 '17 at 20:34
  • @TimHargreaves I don't quite get what you mean by "powers of turns". – Ruslan Feb 25 '17 at 20:49
  • We are saying that Flux Linkage is in Weber-Turns but by your logic, the flux of one turn is in Weber/Turns so by multiplying once by the number of turns, our unit has an extra Turns^2 in it. – Tim Hargreaves Feb 25 '17 at 20:53
  • @TimHargreaves by definition, weber is a unit of magnetic flux, not weber/turn. Starting from this definition, we find that flux linkage has unit of weber-turn, since it's flux times number of turns. Note though that a turn is rarely used as a separate unit, so in most texts (outside of your studies) you'll see that it's used as a unit for both flux and flux linkage. You just need to understand that it's not the only possible way of working — you can always introduce as many auxiliary (dimensionless) units as you need. – Ruslan Feb 25 '17 at 21:05
  • I'd like to clarify why it's OK that for apples we say gram/apple while for magnetic flux it's simply weber. Weber here can be viewed as a single name for a ratio of some "schweber" and turns. Similarly, we could define gapfel=gram/apple and speak in terms of gapfel instead of the ratio of gram and apple. It's just a matter of definition. – Ruslan Feb 25 '17 at 21:15
  • I apologise for going on but I would really like to get this in my head. 1) You say that by definition the unit of magnetic flux is Weber - fine, I agree. By definition, isn't the unit of mass grams? I'm fine accepting that it's okay to just define things however and we just choose to nice ones but it sounds like your are implying one SHOULD be Webers and the other, grammes per apple and I don't see a difference of why
    1. Also, you say that you can always introduce dimensionless units. Okay, so can I measure angular velocity in hertz since I can cancel out the radians in radians per second?
     – Tim Hargreaves Feb 25 '17 at 21:44
  • @TimHargreaves 1) Yes, the unit of mass is gram. And now you want to distinguish total mass and mass of a single apple. You define your new unit of "specific apple mass" as gram/apple. Then you have to correspondingly take into account the unit of apple in number of apples. 2) Right, you could. Some would intensely object to this, but technically this is correct. You just have to not forget where the factor of $2\pi$ belongs and where not. Similarly you could say that e.g. rotation frequency is measured in revolutions per second, but really it's still good old hertz. – Ruslan Feb 26 '17 at 05:30
  • The weber is the SI using of magnetic flux. The weber-turn is a practical (but not SI) unit of magnetic flux linkage. These are two different concepts, which becomes clear if you consider components like memristors! There is a similar units analogy between the amperes and ampere-turns. But whatever the rights and wrongs of the situation, picking a fight with your examination board is not a good plan. – alephzero Feb 26 '17 at 06:13
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It depends what you mean by real unit. It is not an SI unit: http://www.ebyte.it/library/educards/siunits/TablesOfSiUnitsAndPrefixes.html

So quite a lot of people wouldnt consider it a real unit. If for some reason a standard body in your country declares it a unit then it is for this country.

If a board of examiners which you have to respond to believes it is, then you better do yourself. At mist you could ask for an official reference.

lalala
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