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# Calculating the strength of an electromagnet with a closed magnetic circuit core

## Calculating the strength of an electromagnet with a closed magnetic circuit core

(OP)
Hi everyone,

I am interested in calculating the magnetic field strength produced by an electromagnet with a core shaped like an O that forms a closed magnetic circuit, shown in the image that can be seen here - http://staff.ee.sun.ac.za/pjrandewijk/wiki/index.p...) Since there is no air gap, I have assumed that the path of the magnetic field is a closed loop through the high permeability material of the core and the field strength the "O core" electromagnet is going to be higher than the field strength of the standard "I core" electromagnet.
I am just wondering if any wiser, more experienced people than myself could tell me whether I am using the right formulas, in the right way - because there is a point that confuses me.

I have found the following two formulas on the page http://en.wikipedia.org/wiki/Electromagnet under the heading "Closed Magnetic Circuit"

This one is for calculating magnetic flux (B) in Tesla
B = NIμ/L

and this one is for calculating the force (F) in Newtons
F = (μ squared * N squared * I squared * A) / (2*μ0*L squared)
Sorry for writing "squared" all the time - problem with my keyboard!

Where
B = Magnetic Field (Magnetic Flux Density) in Tesla
N = Number of turns of the wire on the electromagnet
I = Current in the winding wire in Amperes
μ = Permeability of the electromagnet core material in Newton per square ampere
μ0 = Permeability of Free Space in Newton per square ampere
L = Total length of the magnetic field path in Meters
A = Cross sectional area of the Core in Square Meters

Can anyone tell me if these are the correct formulas to use here?
The thing that confuses me is the L value - Total length of the magnetic field path in Meters. The formula seems to say this value should be the entire length of the core, and the attached image seems to say this as well. If I use this length, I do not see how the Turn Density of the winding wire can be derived. If the length value is just the length of the area of the core with the windings, I can see how the Turn Density can be factored into the equation, but using the entire length seems to eliminate the Turn Density is a factor - which seems incorrect.
Can anyone suggest how to get a value for L?

Thanks and all the best!

### RE: Calculating the strength of an electromagnet with a closed magnetic circuit core

You have N turns around your core. It won't matter if they are closely spaced (high turns density) or evenly spaced around the core (low turns density); you'll get the same inductance either way. At least until you start taking parasitic effects into account at higher frequencies...

Z

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