I'm trying to write a fantasy scifi story about magic being just another form of energy. It would be like electricity but with a few quirks. I am going to base the "power limit" (basically how much magic a person would be able to safely manipulate) on how much energy is required to kill a human via 1.) Electricty 2.) Heat 3.) Ionizing(?) Radiation 4.) Plain old blunt force
Generally a current through the heart between 100 and 200 mA is considered directly lethal with very little chance of survival. Note that higher current actually raises the chance of survival as the muscular cramps inhibits the heart from going into ventricular fibrillation.
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Now, skin has a complicated voltage-current-resistance relationship, but if we consider a macroshock of about 220 V
50 Hz applied on relatively large areas (i.e. ex. palms, or palm and sole) of wet skin on two major limbs, where there is no forced penetration of skin, an impedance of around 1400 Ohms is reasonable.
That gives us ~150 mA, right in the deadly range. That gives ~34.5 W, so ~34.5 J/s. One second of exposure is most probably lethal. If applied directly to the heart, a lot less is needed to kill.
This formulation doesn't feel quite right for r/AskScienceDiscussion but the question is fun and I have time am procrastinating. If highly trained wizards have very precise control over the application of magic then killing a person doesn't take much:
Disclaimer: math has been half-assed
If you boiled the medulla oblongata, my guess is about 50 grams of tissue, heated to 100 oC from 37 oC, or 50x63x4.184 = 13,179 Joules.
This is the approach I like, but if OP really wants to cheap out on energy use they might get away with heating 1 g of medulla from 37 to 60°C, about 84 J (estimating brain specific heat capacity 3.65 J/gC).
There's a substantial difference between the energy needed for dead eventually, dead soon, and dead right there.
The dose for "immediate and permanent incapacitation" is about 8,000 rads. This was important knowledge for Cold War neutron weapons. It's also a high estimate - 400 rads will probably kill you eventually, but not without a weeks-long "walking ghost" phase where you can still walk around and do things while lack of cell division and a damaged immune system slowly catch up to you. 8,000 is the dose where your nervous system stops functioning properly and you probably never get up again.
Rads are an absorbed dose of 0.01 J/kg of ionizing radiation so for a 100 kg adult that's about 8000 J. A 5.56 55 gr from a long barrel is about 1,300 J.
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Air will absorb half the radiation every few hundred meters depending a little on type so it's not really a sniper weapon. You also don't want even a tiny amount backscattering off the target and onto you or they're dead right there and you're dead eventually.