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Honestly, I only really see wizards losing immediately in England, lol. It's canon that many wizards can use spells silently and/or without a wand, and some even create their own spells; they could likely incapacitate a soldier (or many soldiers, depending on the spell) without raising suspicion by having to aim a wand or gun.
I dunno, Magneto gives the US Army a run for their money in X-Men - I would think a similarly talented or experienced wizard would have comparable powers.
True enough, the capabilities of Magic haven’t been explored enough canonically to disprove that - but if the government learned of Magic, the first thing they’d do is subvert some wizards to their side, who might be able to counteract them - in many ways, it’s a battle of statecraft as it is of actual power.
I don't disagree, but I also don't think that that's enough on its face to determine with any certainty that muggles would "win" whatever conflict arose. An army would definitely have a tactical advantage, but wizards are presumably educated in order to be self-sufficient and many of the creature comforts they're accustomed to can't actually be acquired with muggle resources - at least from what we see in England, they have their own political systems, press, and currency.
But they were able to setup the core of their commercial and governance infrastructure in the middle of London, with no particular notice from muggles - not to mention, we know that the government already knows about wizards (MoM liaises with the PM). So there must be a quid pro quo already in place, with the government tolerating and aiding in the existence of a semi-independent polity in their heartlands in return for unspecified benefits, probably defence against foreign wizards.
Magneto is uniquely capable of stoping most weapons. I don’t think that is a good comparison.
Magnetism’s just magic anyway. Who can explain that shit?
Easy. Just imagine a ball of uniform charge distribution that's spinning, and add relativity. Except it's not a ball, isn't spinning, and doesn't really have a defined location or speed so good luck with the relativity bit.
Me, but it's a secret.
The greatest problem you would have fighting the Wizarding World is there is no easy way to tell who your enemy is. You'd be fighting an insurgency that can just vanish into thin air, with some pretty potent abilities.