I want to devise a simple procedure that can be followed by students to discover that a current in a wire produces a magnetic field near that wire.
I am of course restricted to very simple materials, but I do have a strong neodymium magnet with which the students magnetize needles, which we then use to discover and map the magnetic field.
I have four $1.5V$ AA batteries connected in series, which yield $5.5V$ (one battery is kinda weak). I'll use 1mm thick copper wire, as well as some aluminum foil and tape to secure the connections. I assume $1\Omega$ resistance (Wikipedia says $0.1\Omega$ internal resistance for a typical AA battery, compared to which the wires should be negligible, so I'd rather overestimate the resistance)
According to my calculations, at a distance of 3cm from the wire (about the size of the needle) this should net me $33\mu T$ of magnetic field, which should be somewhat detectable by the needle, considering it visibly picks up the Earth's magnetic field which is $65\mu T$ again according to Wikipedia.
However, the needle does not seem to care one whit about the current in the wire.
Did I mess up my calculations, or did I make a mistake in my setup?