# Calculating the magnetic field of a closed magnetic circuit

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 attached image that can also be seen here - (http://staff.ee.sun.ac.za/pjrandewi...uctor_magnetic_circuit_with_ungapped_core.png) 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 people than myself could tell me whether I am using the right formula, in the right way because there is a point that confuses me.

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

This is for calculating magnetic flux (B) in Tesla "For a closed magnetic circuit".

B = NIμ/L

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

L = Total length of the magnetic field path in Meters

The thing that confuses me is the L value - Total length of the magnetic field path in Meters. I thought I needed to include the Turn Density of an electromagnet when calculating the field strength, but this formula seems not to include the Turn Density.

The formula seems to say the L value should be the entire length of the O shaped core, and the attached image seems to say this as well. If I use this as the 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 as a factor - which seems incorrect. Can anyone suggest how to get a value for L?

Thanks!

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The turn density is hidden as N/L.
Where along the length the turns are does not matter (much), so 10 turns close together and 10 turns spread out give the same result.