Slughorn explains, when everyone is assembled, that alchemy with an egg is actually where phoenixes are speculated to originate; but no one has the recipe any more and there haven't been new phoenixes for centuries. They will not be making living things today. But the eggshell is a good base from which to appear lots of possible objects; alchemy doesn't like to conjure things into existence in plain sight but is quite willing that new things appear inside eggshells, cocoons, geodes, and similar. Their eggs have been pre-drained of their interiors for this purpose, although some recipes use full eggs.
As last week, they are invited to come up with recipes on paper for review by the professor before trying anything. Known possible results available with this set of ingredients include wooden, decorated eggs nested inside the shell; a shellful of small sharp teeth (the commonest source of hens' teeth, as they have encountered once or twice in potions); successively smaller eggshells the smallest of which holds a blob of mercury; and a perfectly hardboiled egg which can be arbitrarily flavored by exact details of the process. But they are welcome to aim at another result as long as their procedure looks safe.
"Oh." Pause. "That actually makes sense. I wonder if I could do magic around one of Dad's sensors and see if they pick anything up before they break."
"Well, I wonder that, too, but if you want to do it legally you have to wait until you're seventeen."
"Yeah, but thinking about it like that, it actually does make fundamental magical research more appealing, combining magic and technology would be great."
"I have no idea how long it takes to set up covert experiments, so maybe you should mention to your dad we want to do this in a few years, Willow."
"I mean, it's not my dad's stuff, the really sensitive sensors are really huge, and CERN doesn't have one of those yet, they started building it last year. I dunno what'd happen with magic around it, but the way these things work is that like... The physicists have this model of how particles work and what they do, and then they're like, 'if we're right about this and we do that, then this will happen,' so they go ahead and do that and see if the thing happens. Like, throwing one particle at another and seeing how much energy's released, I guess, or something. And if they get it wrong they spend a while trying to figure out why and coming up with new things to test."
"Yeah, but we don't even actually have any observations in order to make a model. Like, we're told technology doesn't work here, but doesn't work how? Does it stop working and resume when away from here? Does it get fried? Does it do different things? Does it become sentient? If it gets fried, where does it get fried, how long does it take to get fried, what gets fried first, how much magic is enough, is long exposure to weak magic the same as short exposure to strong magic, et cetera."
"So, Willow, get your dad really excited about all these questions and promise him we'll make careful observations if he mails us gadgets."
"I don't think there's actually a rule against it, just, you know, it'll break so why would you."
"I think Mr. Maxwell will probably have a better idea than us about what things are easy to observe and cheap enough that he doesn't mind owling them to Hogwarts."
"I suppose so. I'm wondering if small things like electronic watches are affected or if it's only more sophisticated tech."
"Well... yes, but there might be a limit to how much he wants to spend on miniaturized electronics for twelve-year-olds to take apart in the hopes that we produce adequate notes."