[investigator2100 (OP)]

I have used Gauss meters. I found that these meters cannot assess real strength of unsaturated magnets. For, a reasonable amount of flux lines of an unsaturated magnet emanate from sideways. A Gauss meter never senses these runaway flux lines.

The same flux lines do not flee when the unsaturated magnet attracts another magnet. While attracting the other magnet, the same runaway flux lines change their path and become a part of attraction force of the unsaturated magnet.

On the other hand, when two unsaturated magnet repel each other, the same flux lines ignore opposite like pole and go on emanating from sideways. Escape of over quantity of flux lines enhances repulsion force between two magnets.

I have recently published a preprint titled, “High repulsion permanent magnet”. This paper relates to this topic.  Link is attached

[alancalverd]

A gaussmeter measures the field in its detector area. You can't blame the meter for your choice of an inhomogenous field! Try putting the sensor in the middle of a long, tightly-wound  solenoid - you should find the indicated field varies very linearly with the solenoid current.

[investigator2100 (OP)]

A gaussmeter measures the field in its detector area. You can't blame the meter for your choice of an inhomogenous field! Try putting the sensor in the middle of a long, tightly-wound  solenoid - you should find the indicated field varies very linearly with the solenoid current.

In 2012, I presented practical comparison of functions of saturated and unsaturated permanent magnets in University of Science and Technology Lahore.

 Extra permeability was added to a saturated permanent magnet to make it unsaturated, by using iron pieces on both end of the permanent magnet.

The professors measured flux densities of both kinds of magnets using a gauss meter. The flux density of saturated permanent magnet was 45 gausses and the flux density of unsaturated permanent magnet was 35 gausses.

Both permanent magnets were interacted using a device. The same electromagnet with the same current interacted with both kinds of permanent magnets separately. Attraction forces of both kinds of permanent magnet appeared to be the same while repulsion force of the unsaturated permanent magnet was nearly double than that of the saturated permanent magnet. It is apparent that actual flux density of the unsaturated permanent magnet appeared only when this magnet faced the electromagnet. Gauss meter failed to read the real flux density of the unsaturated permanent magnet.

Iron core is added to air core solenoids to add permeability. I have applied the same process on permanent magnets. Adding an iron piece to a permanent magnet enhances permeability of the permanent magnet. So the permanent magnet becomes unsaturated. This is not an odd choice. It is application of a well-conceived process. 

[alancalverd]

Adding iron to the poles of a magnet may or may not desaturate the core, but it will certainly distort the near field, so you will get a different (lower, in the simplest case) reading on the gaussmeter.

We measure very small environmental  field strengths by putting a Hall probe between two large frustrated pyramidal blocks of soft iron

                                                  [≡]> | <[≡]

so the probe field is the external field mutiplied by the ratio of pyramid base to tip area. If you put a small magnet in the centre of the assembly, you will measure a symmetrically reduced field outside the blocks.

[investigator2100 (OP)]

Adding iron to the poles of a magnet may or may not desaturate the core, but it will certainly distort the near field, so you will get a different (lower, in the simplest case) reading on the gaussmeter.

We measure very small environmental  field strengths by putting a Hall probe between two large frustrated pyramidal blocks of soft iron

                                                  [≡]> | <[≡]

so the probe field is the external field mutiplied by the ratio of pyramid base to tip area. If you put a small magnet in the centre of the assembly, you will measure a symmetrically reduced field outside the blocks.

Your first answer seems to conclude that magnetic field of an unsaturated permanent magnet is inhomogeneous. This conclusion produces another question.

Electromagnets (iron-core-solenoids) are designed, usually, to remain unsaturated while working. So, magnetic fields of unsaturated electromagnet should also be ‘inhomogeneous’.

Moreover, some part of the iron-core always remains out of coil. So, shape of an electromagnet resembles to that of iron-added permanent magnet. This fact also prove that the magnetic field of an electromagnet is ‘inhomogeneous’.

Is magnetic field of a usual electromagnet not suitable to be measured by a gauss meter?

[alancalverd]

A gaussmeter will accurately measure the magnetic field at its measuring point  - usually the center of a circular coil  or a square Hall probe. You can believe the result, but it won't represent the field at any other point in the universe.

Obviously the external field of any magnet is inhomogeneous because there are other magnets in the universe and even if there was only one, its field must decay to zero at infinite distance. It is extremely difficult to produce an adequately homogeneous field for magnetic resonance imaging over a large area: superconducting solenoids offer near-ideal physics over a small area at the expense of considerable thermal engineering and exotic materials, and electromagnets offer parallel field lines over the diameter of a human body at the expense of considerable electrical and mechanical engineerin.  Permanent magnets turn out to be too temperature-sensitive for most clinical purposes.

The required degree of homogeniety depends on the purpose of the magnet, and if you want it to lift scrap metal or attract an armature from a distance, a converging field is usually an advantage.