Electrical – Calculation of magnetic field saturation inside coil core

A simple model to help you visualize: The magnetic flux forms loops, you cannot have a magnetic field line terminate on nothing in free space. That means that all those flux lines inside the solenoid heading (for example) to the right. The flux line must continue outside the solenoid and loop around to join the other end of the flux loop. In doing so it heads to the left. No external flux lines -> no flux.

So what could be the issue?

1) In an infinite solenoid, there is no external magnetic field. One example of this is a Tokamak or toroidal solenoid. Like a big doughnut. The flux lines form loops within the doughnut and have no need to go outside. - of course a mathematically ideal infinite solenoid could have been what they were discussing, in which case the field lines loop around infinity. Hard to test though.

2) The flux density outside of the linear finite solenoid is much less than inside. So while there may be X flux across the throat of the solenoid that same amount of flux (X) is spread out over a much much larger cross sectional area. The density is much less. [here the area is the cross sectional area across the solenoid.]

3) Perhaps they are talking about a shielded solenoid? This would involve having a high permittivity material external to the coils to trap the flux lines.

There is some confusion here since you state that the gyroscope is giving you readings where the software indicates that it is the gyroscope that wasn't initialized.

The accelerometer is integrated into the same chip as the magnetometer which on that breakout board is a STM LSM303D(datasheet ). This chips contains a MEMS type magnetic field sensor. STM is secrative about the exact type of sensing element, it is likely that it can be succeptible to damage at strong magnetic fields and the high flux density and divergent field lines close to the surface of a magnet may cause other damage.

The surface or rare-earth magnets (e.g. neodymium) can have considerable field strength near the surface, if you bring the magnet very close to the sensor the field strength can be a significant fraction of 1T and there may be enough flux density to significantly damage a sensitive device like a mems sensor.\$1000\mu\ T\ = 10 G\$ which the magnetometer datasheet says should be fine, but I suspect the strength of the field was a good deal higher. The constant readings and software error message is likely indicative of damage to the relevant sensor chip the readings being garbage data or default values from an uninitialized sensor.

In general there are any number of ways that a strong magnet close to the board can cause damage to one of the sensor chips. A uniform 1milliTesla field is probably less damaging than the highly divergent field at the business end of a magnet.

The magentometer/accelerometer should handle magnetic fields up to 10,000 G according to the datasheet, however I suspect that the gyroscope (the device giving you an error message) with its mems gyroscopic sensor (likely a PZT but STM doesn't say) may be more susceptible to damage (datasheet).