The magnetic field of an electric motor only does any useful work when it is inside the motor. There is no stray flux that would be usefully detectable.

Also, magnetic fields don't self propagate, really. That means they fall off extremely quickly with distance unlike electromagnetic waves.

If they use the "air gap" to separate the dry side from the wet side (stator from rotor) one may be able to mess it up by dropping a cloud of iron containing abrasive particles. They'd be drawn into the gap and grind away. Depending how it's constructed of course.

Magnetometers are already used to detect submarines [0]. Maybe it isn't so much about the flux from the motor being detectable, but it's additional interference with the Earth's magnetic field.

[0] https://en.m.wikipedia.org/wiki/Magnetic_anomaly_detector

They're used to detect the hull, which is why Titanium is valuable for use in military submarine hulls as its non-magnetic. Fun fact, much of the Titanium used in US submarine hulls was sourced from - er - the USSR. The needed the foreign exchange more than it was worth denying the Titanium to the US.

Read a book recently called "Big Ear" by John Krauss. He talks about degaussing ships in WWII since Germany was using magnetic mines.

Ah, but it does propagate. A time varying magnetic field generates an electric field. Though as you said, the motor does not make an efficient antenna.

The electric field gets quickly attenuated in saltwater though, especially at high frequency: https://en.wikipedia.org/wiki/Communication_with_submarines

Yep, but that E field is generated from currents in the lossy seawater, and those currents are induced by the magnetic field. If the seawater were a perfect conductor, the magnetic field would not propagate either.

Free space impedance is 377 Ohms/meter; the ratio of E/H fields. Seawater is much, much lower, but the ratio is still there. If there's a propagating H field, there is a corresponding E field; that's the law according to Maxwell.

The VLF antennas on the subs are trailing wires; electrically short dipoles. Those are mostly sensitive to E fields.

Maybe especially in seawater?