# Electromagnet Design - Value of inductance L

1. Jul 13, 2012

### EEE12

1. The problem statement, all variables and given/known data

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 lets 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.

2. Relevant 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

3. 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

Last edited: Jul 13, 2012