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Homework Statement
Hi all,
I am working on an electromagnet design. It is a C-shape with an air gap of 80mm. The number of coil windings is 320 turns. I would like to generate let's say B = 30 mT = 300 gauss in the air gap. Area of air gap Ag = 80mmX80mm = 6.4e-3. Mean length lg of electromagnet is 80mm.
Homework Equations
mmf (F) = Flux ∅ X Reluctance R
Flux ∅ = Magnetic field density (B) X Area of air gap
mmf (F) = no. of turns N X magnatising current (I)
Hence,
I = B.Ag.R/N (∅ = NI/R)
induced voltage ε = -N d∅/dt = -L di/dt
therefore,
L = N^2/R
on the other hand,
Ztotal = V/I
Resistance of the coil is too small therefore I assume that Load is purely inductive.
Ztotal = 2pi.f.L
so,
L = Ztotal/2.pi.f
The Attempt at a Solution
Total Reluctance R = Reluctance of Air gap as the reluctance of the core is negligible.
Reluctance of Air gap = lg/μ.Ag = 80mm/(4.pi.e-7X6.4mm^2) = 9.95e6
I = 30mT X 6.4 mm^2 x 9.95e6 / (320) = 6 A
L = N^2/R = (320)^2/9.95e6 = 10 mH
Vrms (AC) = 240 V, I = 6A, f = 50 Hz
Ztotal = 40Ω
L = 40Ω / 2.pi.50 = 127mH
Why are the values of L different? The difference is a factor of 10 which is significant. There must be an explanation which I seem to be missing. Hope you can help.
Thanks
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