Relationship between flux density, MMF and core area - Page 1
Forum section: electronics / beginners

author: ZeroResistance
author_rank: Frequent Contributor
timestamp: October 31, 2018, 08:47:55 am
content: Lets say i have a core area cross section of 1cm^2And MMF I give is 100AT and due to this MMF in the core area I get a magnetic flux to flow which inturn causes a flux density B in the core.Now if I double the core area to 2cm^2, but would keep the MMF same that is 100AT, how much would the flux density B change to?My original guess was the B will halve, but I guess increasing the core area also reduces the reluctance of the core so more flux would flow for the same MMF.So I would like to know the relationship between these 3 quantities?

author: spec
author_rank: Frequent Contributor
timestamp: October 31, 2018, 05:57:02 pm
content: + ZeroResistanceBit of a head scratcher, but I will have a go at answering your questionThe reluctance (Rm) of an inductor is, l/µAwhere:l is the length of the magnetic circuit in the coreµ is the permeability of the core materialA is the cross section area of the core.So, if you doubled the cross section area of the core, you would half the reluctance, as you say.It you half the reluctance you double the flux which means that, as the core cross section area has also been doubled, the flux density in the core would be unchanged, as you thought.There is a further consequence of doubling the core cross sectional area: the inductance would also double, which means that the reactance, XL, would double (XL= 2ϖfL), which means that if you were pushing an AC constant current through the inductor, the voltage across the inductor would also double.One thing that often causes confusion with inductors is that reluctance resists the magnetic flux in the core, but reactance resists the flow of electrical current in the inductor's coil. The two parameters are not the same. In fact, far from it: if you half the reluctance you double the reactance.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 31, 2018, 08:39:43 pm
content: What mu and path length?If everything stays the same, you're just stacking two cores, using the same magnetization for each. Doesn't matter if they're stacked or alone, you're just asking if it's two together, so the total flux is double of course.Tim

author: spec
author_rank: Frequent Contributor
timestamp: October 31, 2018, 09:37:55 pm
content: Take a cold shower Tim- you will feel better

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 31, 2018, 10:59:28 pm
content: You covered it in much better detail so I don't have much to add... I just wanted to get my shoe inTim

author: spec
author_rank: Frequent Contributor
timestamp: November 01, 2018, 02:50:47 am
content: Nice of you to say soIt had been a long day for me!

author: ZeroResistance
author_rank: Frequent Contributor
timestamp: November 01, 2018, 03:04:41 pm
content: Quote from: spec on October 31, 2018, 05:57:02 pmthis is an interesting insight!! Thanks for sharing!Also lets not forget that scaling a core up will also affect the average path length the magnetic flux has to travel and that would have an overall negative effect on the flux as area would have a positive effect.but anyway probably I got the answer to my question that the flux would double with area and B might remain the same.But then that would mean both the cores will satuate at similar MMF values even though one is double the area than the other.

author: ZeroResistance
author_rank: Frequent Contributor
timestamp: November 01, 2018, 03:06:26 pm
content: Quote from: T3sl4co1l on October 31, 2018, 08:39:43 pmFlux would probably double but B would remain the same wouldn't it?Having said that to have a high attraction force what is necessary1. more B or2 more flux

author: T3sl4co1l
author_rank: Super Contributor
timestamp: November 01, 2018, 06:40:25 pm
content: Flux I guess?The Maxwell stress is \$\sigma = \frac{B^2}{2 \mu}\$, in units of pressure (or energy density -- same thing). If you have an air gapped core with so-and-so B in it, and ~no field outside the core, then this is the force pulling the gap together. Or if you have two magnets pole to pole, then this is the pressure pushing/pulling on them (minus the pressures at the opposite ends, mind: there is a net pressure when they are unbalanced, of course).Flux goes as \$\Phi = B A_e\$, but force also goes as \$F = \sigma A_e\$, so we can also say \$F = A_e \frac{\Phi^2}{{A_e}^2 \mu}\$ and one Ae cancels so it goes as flux squared per area.It's like asking, "which matters more, the voltage or the charge on a capacitor?" They're both fundamental quantities to the element, and the question implies more about the ignorance* of the one asking it, than its  answer reveals about the subject.(*Not stupidity. Ignorance is good, in that it's why we ask questions. As opposed to "you can't fix stupid".)Flux isn't usually too important, for mechanical purposes, because you can almost always wait a little longer. A solenoid might take 500us to charge up, but 5ms or more to actually move. If it's not moving fast enough, you can increase the voltage, or goose it with some pre-drive or PWM it for constant current drive (as done with stepper motors).Or how relays are usually noticeably slower to turn off when shunted with a diode (e.g., 20 or 30ms, on a relay that's nominally rated for ~10ms opening time). Easy enough solution there, use a zener instead of a diode to clamp the flyback. Dumping the flux into a higher voltage equals less time.Tim

author: spec
author_rank: Frequent Contributor
timestamp: November 02, 2018, 05:51:05 am
content: Quote from: ZeroResistance on November 01, 2018, 03:04:41 pmNo probsIncreasing the core cross section can increase the path length, but not necessarily substantially, take the case of a toroid for example.There are a few counter intuitive aspects to inductors (and transformers). Your point about the core saturation does seem strange.Another insight is that if you have an inductor with a constant AC voltage across it and you double the core area, you double the inductance and therefore half the current. This halves the MMF. So you have double the core area and half the MMF which means that you have one quarter the flux density in the core.