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Electrical Engineering/Factors affecting inductance

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Two inductor cores
Two inductor cores  
QUESTION: Hello Cleggsan,

I hope this message finds you well.
I was wondering if I could ask you a question on the Inductor design. I hope it is not too basic.
I have been reading here

http://www.allaboutcircuits.com/textbook/direct-current/chpt-15/factors-affectin

that, along with the core material and the number of turns in the coil, two other factors affecting inductance are coil length and coil area. It says that greater coil area will result in higher inductance, but that ”the longer the coil’s length, the less inductance; the shorter the coil’s length, the greater the inductance.”

I have been trying to understand how these points would relate to two inductors, one with a thicker core than the other, as shown in the attached image.
Each has the same number of turns and the same core material.
Inductor A has a shorter coil length but smaller coil area.
In the case of Inductor B, the coil area is greater, but it seems that the coil length must also be longer, given that is has to be wound around a larger diameter core (and in this case, I guess the resistance of the wire of the coil must also be greater).
Which one would you expect to have greater inductance here? Would the difference between them be great? Are there any other factors I have neglected to address?

Thanks as always Cleggsan,
Arigato gozaimasu!

ANSWER: Nice to hear from the happy inventor.

Inductance would be greater where the core is more volumetric because the magnetic field created from the 5 amps of current would be more greatly induced.

The difference in inductance is a function of the volume of the iron core.  I would not expect the difference to be great due to the physical difficulty and practicality of designing such cores with similar windings and core similarities.



---------- FOLLOW-UP ----------

QUESTION: Thanks for the answer Cleggsan.
So, if I understand correctly, an inductor with a thicker core will generate a stronger magnetic field/higher inductance?
If this is correct, then is there a point at which making the core thicker would no longer cause a higher inductance? If so, would a thicker core at this point actually equal less inductance, given that the coil length has still increased, and I assume more current is being "spent" in the coil without a corresponding increase in inductance in the other coil that I want to induce a current in?
If this is a reasonable understanding of the situation, is there a way to estimate how thick the core can be made relative to the coil and still gain inductance?
I'd be really interested to know about the thickest core inductor you have seen.

I still feel my grasp on this topic is shakier than I'd like, so please excuse me if I have laboured the point (or misunderstood!)

Arigato gozaimasu!

Answer
It is a non-linear function.  That is, doubling the size of the core will not double the inductance of a given coil; tripling the core size will only increase the inductance little over the double size.

And the permeability of the core is an important function as well.

Much of magnetic circuit theory is experimental or laboratory measurements on actual coils and cores because the mathematics is good only for theoretical designs that are easily simulated.

In fact the design of coils both with and without metal cores is as much an art as it is a science.

Domo domo.  

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cleggsan

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