There's a small pile (maybe 2 tablespoons) of fine black powder that's fallen out of the T&P valve discharge pipe on my electric water heater. I'm hoping to find out its source and ramifications so I can determine what to do about it. The T&P valve is not leaking - the powder is bone dry, almost like soot. I haven't noticed any black sediment coming from the faucets.

Could be spider or insect droppings, roaches make black sand like droppings. If the washer was to decay that much, I think it would be leaking. Here is a procedure to use BUT be aware it may not close properly and you will need to turn off the water and replace the valve.

To test the valve to ensure that it's working properly, simply raise and lower the test lever several times so it lifts the brass stem that it's fastened to, the spring should close it. Hot water should rush out of the end of the drainpipe. If no water flows through the pipe or you get just a trickle, replace the valve. If it leaks after testing, flip the lever a couple of times. If it still leaks, replace the valve.