Electromagnet Design - Value of inductance L

[EEE12]

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

 

[anathema]

for sharing your problem! It seems like you have made some good progress in your calculations, but there are a few things that may be causing the discrepancy in your values for L.

First, it's important to make sure that all of your units are consistent. In your calculation for reluctance of the air gap, you have used millimeters (mm) for length and square millimeters (mm^2) for area. However, in your calculation for L, you have used meters (m) for length. This could be causing a significant difference in your final value for L.

Secondly, it's important to consider the frequency of the AC current that you are using in your calculations. In your calculation for L, you have used a frequency of 50 Hz. However, in your initial calculation for mmf, you have not specified a frequency. Depending on the frequency, the inductance of the coil may change, which could be causing the difference in your values for L.

Finally, it's important to consider any other factors that may be affecting the inductance of your coil, such as the material of the core or any other components in the circuit. It's possible that these factors may be contributing to the difference in your values for L.

I hope this helps and good luck with your electromagnet design!