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at school, I learned that the magnetic field strength(H) is defined by the Number of turns*current/Length. is the length in the formula the length of the coil or the core? so if an iron rod is 10cm long and only half of it is wound with 10 turns of wire with 1 amp flowing, will the magnetic field strength be 100A/m or 200 A/m? or if a small part of a toroid is wound, would the length be the circumference of the toroid or just the part that is wound with wire? Thank you

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The relevant length is the length of the entire magnetic circuit.

In the case of an iron rod, this includes the return circuit outside in the air. This return circuit dominates the reluctance of the entire circuit. So in this case, it doesn't really matter whether your turns round the rod are uniformly distributed along it or all at one end. You would have to integrate over all paths (small ones close to the iron, and big loopy ones further away) to find the total flux and so the effective magnetic length. However you can get a ballpark, order of magnitude, figure by ignoring the length of the iron, and taking the length of the air, so 10 cms. Your H field through the air has been roughly doubled by using the iron rod within the solenoid.

In the case of a toroid, the core is homogenous and so much easier to handle accurately. The magnetic length is the circumference of the core.

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In general, you have to integrate over the fields to get the length equivalent for the given geometry (core and winding). Only special cases give a simple result with a trivial geometry factor (like "thin solenoid" or "uniform toroid").

For a high-permeability core, the flux density (B) is concentrated in it, and the effective length is the mean path of the core. H however still depends on the current distribution.

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