Induced voltage and current question

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Main Question or Discussion Point

I have been trying to calculate the voltage and current induced in a stator by a rotor of permanent magnets. The formula Length x Velocity x the B-field , i understand most of. My question is about the Length part of the formula, in a stator the wire passes through the iron core, so is the length that the formula refers to the small section that passes though the iron core or is it the total length of the wire in each phase of the 3 phases in the stator? As an example: if the velocity was 13.5 m/s and the B-field was 6500 gauss and assuming that the length is total wire length of the phase was 76m, i get 13.5m x .65 T x 76m = 666 volts but that doesnt look rigth to me. any help would be greatly appreciated
 

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  • #2
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I believe i have figured out the answer to my question. THE B-field is contained in the stator core and since the permeability of air is very poor ( like 1 i believe) the field only affects the wire that passes through the stator core, so its not total length of the wire in each phase, but only the wire that passes through the core. If this is correct, it leads me to a new question about the length of the wire: would i multiplythe length of wire that passes through the stator times the number of wires in each coil? could someone tell me if im right or wrong please.
 
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What counts is the area of the stator iron core around which the stator coil is wrapped, times N, the number of turns around the iron core, times 2, because the field in the iron core switches from + 0.65 Tesla (use MKS units) to - 0.65 Tesla every cycle. This is for each phase voltage. Are you making a wind machine dynamo with a flat-plate rotor of alternating polarity permanent magnets and an axial B field? Keep air gaps to a minimum.

Bob S
 
  • #4
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Hi everyone, ive been looking into faradays law of induction on the advice of Bob and a question about the equation. In the attached picture, the AC generator example, how is the area calculated? Im not exactly following the meters squared per second part? i looked up the definition on wikipedia and understand that its speed or velocity defined by distance in meters per second. Is the Area the total distance traveled by the rotor in one second? any help is appreciated.
 

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We will analyze the illustration in the lower right of your thumbnail (generator armature), using Faradays Law, as written in the middle left.

Use
N=100
B=0.4 Tesla (static field)
A = 5 cm by 5 cm (=0.05m x 0.05m = 0.0025 m2) rotating coil
RPM = 600; rps = 10 Hz; ω = 62.8 radians per second.

So V(t) = -N·d(B·A)/dt = -N·B·dA/dt = N·B·ω·A·sin(ωt)

=(100)(0.4)(62.8)(0.0025)sin(ωt) = 6.28 sin(ωt) volts.

Bob S
 
  • #6
We will analyze the illustration in the lower right of your thumbnail (generator armature), using Faradays Law, as written in the middle left.

Use
N=100
B=0.4 Tesla (static field)
A = 5 cm by 5 cm (=0.05m x 0.05m = 0.0025 m2) rotating coil
RPM = 600; rps = 10 Hz; ω = 62.8 radians per second.

So V(t) = -N·d(B·A)/dt = -N·B·dA/dt = N·B·ω·A·sin(ωt)

=(100)(0.4)(62.8)(0.0025)sin(ωt) = 6.28 sin(ωt) volts.

Bob S
Hi I read through your discussion and seem to think that this might be slightly similar to my question. ( rotating coil in a magnetic field )

And the equation that I have been trying to use limits me as I do not know the length.

The picture on the bottom right mentioned. Is Vgenerated the same as Vinduced?

V/L = c x B

c being the speed
B field
L lenth of wire

Here is the question:

The plane of a 5 turn coil of 5mm² cross sectional area is rotating a 1200 r.p.m in a magnetic field of 10mT.

Any info whould be great.

Lee
 
  • #7
Using this equation I get

So V(t) = -N•d(B•A)/dt = -N•B•dA/dt = N•B•ω•A•sin(ωt)
V(t) =(5)(10x10^-3)(125.66370599999999)(5)sin(ωt) = 31.415 sin(ωt) volts

And using the following, saying t = 60 sec

Then φ = N.B.A φ = 5×10×10^-3 ×5 × 10^-2
φ = 2.5 ×10^-3

And V = dφ/dt or N.A. dB/dt = 4.17x10^-3 V

My concern here is that 1200rpm was not used.
 
  • #8
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Thank you for the explaination Bob, i understand that part of calculating the induced voltage now. In the example, the freqency is for 1 pair of poles. Does the frequency increase as more pole pairs are added?
 
  • #9
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Well, now that i understand how to calculate the induced voltages in the stator, im having a problem understanding how to position the magnets correctly. I am going to use 12 magnets (6 pole pairs), by dividing 360 degrees by 12 magnets i get 30 degrees for each magnet. Using the stator diagram as reference, 30 degrees for each magnet, the magnet covers one side of each coil in all three phases, is that the correct placement? any insight would be appreciated
 

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