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12th September 2005, 10:23 PM  #1 
diyAudio Member
Join Date: Nov 2003
Location: England

Calculating flux densities via induction
Hi,
Okay I have a quick quiz question! I have coils of wire formed into inductors. Usually the inductors act as a sense coils, picking up changes in magnetic flux. I'd like to be able to make a rough guess at the actual flux density that the coils are detecting rather than just quoting a floating value of induced voltage differential. Properties I know about the inductors, their; Inductances Iron / steel cored Lengths Number of turns Crosssectional areas, although they're not circles Frequency of the flux changes they're sensing Range of voltages created across it during use Approximate DC resistance Q factor That the flux density has a permanent value around a few hundred to a thousand gauss and is changing in a roughly sinusoidal way over the inductors From some combination of those factors, preferably the simplest, I'd like to be able to take a guess at the actual flux density changes. Actually, if anyone knows of any Excel sheets for magnetic calculations that'd be excellent! 
13th September 2005, 05:28 PM  #2 
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Join Date: Apr 2005
Location: Nijmegen!

You don't look familiar with Maxwell's beautiful equations, with which you can solve this perfectly well:
With a closed loop you can measure the flux change per time unit through the loop. The formula is as follows: If you now assume that the flux doesn't change over the core's surface, then you can change the first integral into a simple multiplication, leading to: E*S = dF/dt In which E is the electrical field in the conductor, equal to V'/epsilon (V' = voltage on one turn; epsilon = dielectric constant of the core), S is the crosssectional area and F is flux. With an Nturn coil, you get a voltage of V = N*V'. Now you can calculate the flux change with: dF/dt =  (V*S) / (N*epsilon) In which V is the voltage you actually measure. Ofcourse, with a simple Miller integrator or something you would be able to calculate 'real' flux values, assuming you know the starting flux. Makes a nice summer holiday project I have no Spice at hand, so here's some Paint art: You'll still need some proper timing and decharching circuitry, but the idea is there... 
13th September 2005, 05:52 PM  #3 
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13th September 2005, 06:21 PM  #4 
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Join Date: Nov 2003
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Thanks for your help Limhes,
I've seen these formulas before but since maths isn't one of my best subjects I always need to check, otherwise I end up following mistakes round for days on end! By dieletric constant do you mean the electronic capacitive dielectric constant or the magnetic permeability of the core? It's just that you mentioned core rather than coil dielectric. Also, does it matter if the cross sectional area of the coil is distorted from a perfect circular loop. Say if it were a square form. What would the units be with this, area in metres squared and flux in Teslas? 
13th September 2005, 07:08 PM  #5  
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Quote:
Quote:


13th September 2005, 08:22 PM  #6 
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Join Date: Jan 2004
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The voltage generated in a loop of wire in volts, equals the rate of change of the flux through the loop (delta BA).
If you have 10 turns,, 1 meter square, and the flux changes at 1 tesla per second, the voltage will be 10 volts. 1 cm by 1 cm...area=10e4 meters. 1 tesla per second...delta BA is 10e4 Tesla meter^{2}/ second.. one turn, 100 uvolts..100 turns, 10 millivolts. Smaller the radius of the coil, more accurate it will show the field due to field divergence, but the lower the voltage produced. Tradeoffs, always tradeoffs.. John
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13th September 2005, 09:19 PM  #7 
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Join Date: Nov 2003
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Would that be;
turns * area * (delta flux / time) = delta voltage? 
14th September 2005, 08:16 AM  #8 
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Join Date: Apr 2005
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Ah, wait, I am going to correct myself though
I have used the formula in a wrong way, sorry! I just took the first I could find using google, which was in some strange form I think. Using it correctly leads to: V =  dF/dt * epsilon / l In which dF/dt is the flux change per second, epsilon same as above and l is the total conductor length in the inductor (i.e. in which the electric field is present). The crosssectional area is of no importance since the flux density is already transformed into flux. The flux change then equals: dF/dt =  V*l / epsilon 
19th September 2005, 01:13 PM  #9  
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Quote:
Area is in square meters delta flux/time is tesla per second delta voltage should just be voltage.. Cheers, John
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