H is the driving force in coils and is ampere turns per metre where the metre part is the length of the magnetic circuit. In a transformer it's easy to determine this length because 99% of the flux is contained in the core. A coil with an air core is difficult as you might imagine.

I think of B as a by-product of H and B is made bigger by the permeability of the core.

In electrostatics, E (electric field strength) is the equivalent of H (magnetic field strength) and it's somewhat easier to visualize. Its units are volts per metre and also gives rise to another quantity, electric flux density (D) when multiplied by the permittivity of the material in which it exists: -

\$\dfrac{B}{H} = \mu_0\mu_R\$ and

\$\dfrac{D}{E} = \epsilon_0\epsilon_R\$

Regarding ferrite data sheets, the BH curve is the important one - it tells you the permeability of the material and this directly relates to how much inductance you can get for one turn of wire.

It will also indicate how much energy could be lost when reversing the magnetic field - this of course will always happen when ac driven - not all the domains in the ferrite return to produce an average of zero magnetism when the current is removed and when reversing the current the remaining domains need to be neutralized before the core magnetism goes negative - this requires a small amount of energy on most ferrites and gives rise to the term hysteresis loss.

Other important graphs in a ferrite data sheet are the permeability versus frequency graph and permeability versus temperature.

From personal experience of having designed a few transformers, I find them tortuous in that I never seem to naturally remember anything other than the basics each time I begin a new design and this is annoying - in this answer I had to double check everything except the units of H!

Yes, the shape of the coil affects the shape of the field.

The most general answer to your question is that each tiny increment of wire produces a circular field around itself, and the overall field around the coil (or any length of wire of any shape) is the sum (integral) of all of those incremental fields. This is not a simple problem to solve in the general case, but we can make some general statements.

In a coil, the current in adjacent turns is going to have the same magnitude, and produce essentially the same field. This means that the space directly between the turns will have zero net field, since the contributions from the wires on either side of that space have opposite signs and cancel each other out.

This means that the strongest field will be found along the surface formed by the overall colleciton of turns. For a helical coil, this would be on the inside and outside surfaces of the cylinder formed by the turns, and for a planar (spiral) coil, this would be on either side of the plane.

## Best Answer

There's a general problem in physics that you can't measure anything without changing it. Any attempt to introduce a measuring instrument into an experiment changes the experimental setup, and so alters the results.

So the aim is to choose a measuring instrument that changes the results as little as possible. For example, a voltmeter is designed to have as high a resistance as possible, so it doesn't add any significant load to the circuit it's measuring.

In the case of iron filings, they are small and either not magnetised, or are only weakly magnetised. The bar magnet, on the other hand, is much bigger and strongly magnetised. So we assume that the iron filings have only a small effect on the field that they are measuring.

You can make any effect smaller, by limiting how many filings you use. Just sprinkle a few around, and they will have little effect. Dump a whole jar full of them on top of the magnet, and you probably have completely changed the field you were measuring.