Hi,
I'd like to ask a question through an example.

I have 2 solenoids:

Solenoid one consists of a 1 Amp conductor turned 20 times around the entire length of a 10cm core.
Solenoid two consists of a 1 Amp conductor turned 20 times around the entire length of a 20cm core.

If I place a piece of metal at the same distance at each solenoid will they both act on the piece of metal with the same force?

I say no, because solenoid 2 is a stronger magnet so it will draw the metal to with a stronger force.

But I have been trying to understand the magnetomotive force and magnetising force.

Magnetomotive force = I.N meaning whatever length, the magnetomotive force will be the same which is described as the "pushing power" of the magnet.

Magnetising force is I.N / Length which means the longer the less intensity of the field which wouldn't also mean the pushing power is less?

 

Hi,

There is a simple way to deduce the answer to this without getting into anything too complicated. We can use a multi ring model of the solenoid. The turns of wire actually create a helix, which complicates things, but if we reduce that construction to one that has multiple rings of wire that are connected in series with zero ohm short lengths of wire, we create a model that qualitatively will behave the same.

Now that we have the simplified model, we can look at one ring at a time and ask what the field is for a single ring that is 1cm from a point along the central exis and a ring that is 2cm from a point along the central axis.
Because a magnetic field decreases with distance, we know the field for the 2cm spacing will be less than the 1cm spacing. That is simple deduction knowing that a magnetic field decreases with distance. We dont even have to know how much it decreases, just that it decreases.

So we know that a single ring farther from a point in space produces a lower strength field, so now we can proceed on to the multi ring case.

If we have 10 rings spaced 1cm apart from each other and we look at a point along the axis 1cm from the end, we have a progression of distances. The first ring is 1cm away, the second ring 2cm away, third ring 3cm away, etc., up to the 10th ring which is 10cm away. So we have rings that produce the same field 1cm away but are at different distances now. If we add the distances we get 1+2+3+4+...+10=55cm total distance.
Now for the coil with spacing of 2cm and 1cm from the test point, we have instead the first distance is 1cm, the second is 3cm, the third is 5cm, the fourth is 7cm, so they are 2*N-1 cm away, so we have the progression:
1+3+5+7+9+11+13+15+17+19 and this totals 100.

So we have two results:
the 1cm spaced coil has a total distance of 55cm from the test point,and the 2cm spaced coil has a total distance of 100cm from the test point.

Since we know that the field decreases (even without saying how much) with distance and one coil has total distance about twice that of the other, we should be able to conclude that the coil with the 2cm spacing produces a lower field strength than the coil with 1cm spacing. Thus it will produce less force.

That was the ring-linear-distance approximation, which does not really provide quantitative results. The following models are meant to get better and better results.

Should we want a more quantitative result we would refer to the Law of Biot-Savart and apply that to each ring in both cases and add the results and then compare the two cases. That's using the ring model and considers the change of field with distance the way it really is in nature.

Should we wish to avoid the ring model and go straight to the more physical helical model, we would have to apply the law of Biot-Savart to each helical coil and then compare the results. That's using the helical coil model.

Should we wish to avoid that model too and go to the infinitesimal filament helical model, we'd have to model the cross section of the wire using infinitesimally thin filaments and apply the law of Biot-Savart to each filament. This is the best model because it takes the shape of the wire AND the shape of the turns of wire into account.

The result from a calculation using Biot-Savart on a ring is a typical exercise in this field and so i am pretty sure you can find examples all over the web for this one. The only thing that changes is the distance from the center of the ring to the test point, so you could use that formula and just apply the different distances and then sum the results. Doing this for each coil would provide a decent way to estimate the field at the test point.

To find the formula for a solenoid, do a search for "Magnetic field along axis of solenoid". You can then proceed to do the calculations for this and come up with a better result. This will also allow you to test the simpler results to make sure they are right.