That said, based on the size of that thing in the photo I suspect it wouldn't damage anything!
It takes a (much) higher fieldstrength to induce voltages that will destroy electronics than what's required to flip the occasional bit without damage.
Lightning can cause EMP like effects by inducing voltage in conductors not directly hit by the lightning.
(This was a 1991-vintage bike - its modern enough that it uses hall sensors not points, but the electronics driving the ignition and the advance curves might even be analog instead of microcontroller-driven.)
its not linear.
either it induces a voltage high enough to cause disruption or it doesnt.
the limiting factor is the voltage not the power (power is tiny)
thats not a case of power falloff. Because interaction with the environment and target is non linear.
for example if it blasts a phone to reset from a few centimeters it could easily drop all calls in a 20 meter radius. but upping the power/voltage 4 times may only add milimeters to the range of blasting the phone to reset because so much is absorbed by the case. but upping the power/voltage 5 times could add a meter to blasting the phone to reset because the case now no longer absorbs enough energy to prevent the interference. Also resonance and harmonics play a huge role in the effect.
All conjecture. but my point is you cant apply school boy physics to the problem because its not a problem they teach in school.
Vehicle disabling EMPs are of great interest to the likes of CHP, and such.
What makes it tricky is that at those low frequencies the antenna elements are very large, and this is what will play havoc with any attempts to make a directional antenna for the AM Band that is still practical to use for the purpose described here.
So in all likelihood you'll end up upsetting all your neighbors instead of just the one you're targeting.
That said: if you're in the US and transmit outside of the ISM bands or at anything above about a few hundred milliwatts of power, you risk the FCC coming down on you with some hefty fines or jail time.
When you're close enough to the towers, you can hear the transmissions on leaves.
Note: I also have a new theory behind schizophrenia diagnoses about trees talking to people.
It's actually touching the tower though.
(and I have no idea how it works)
That has a chance of working due the very fast rise time you might be able to induce a sufficiently large voltage to cause some actual damage, it will be a 'one shot' affair though. But anything involving regular coils and some push button arrangement will likely cause it's own insulation to break down long before it will do damage to a phone.
That's one of the reasons the spark gap is there in the first place, without it you'd hit the limits of the coil insulation very quickly.
Spark gaps are a pretty nasty way to generate EM interference so there is some truth to the story.
But even with my plasma cutter (12.5 KW, so not the smallest in the catalog) and stick welder I never managed to crash a cell phone.
The plasmacutter did have the habit of resetting the controller until I properly decoupled all the lines into it.
(Note: all memories and calculations are from Burningman a decade or so back - and should be treated with an entire playa-ful of grains of salt.)
(This was the same crew of people where the discussion one night went "We're all on mushrooms, you've just been drinking tequila all night - that means you get to fix the flamethrower"...)
That's really interesting with respect to your plasma cutter.
Seriously though... can you imagine how many laws you'd break using that? The FBI would hang you up by your pubic hair, tar, and feather you.