I would like to build a current source to generate a square wave signal. The amplitude should alternate between 1mA and -1mA every millisecond. I'm thinking of using an LM334, but I'm not entirely sure how to generate the negative current. I would greatly appreciate some ideas and thank you in advance.
Are you familiar with Ohm's Law (which defines the relationship between voltage, current, and resistance)?
The resistance through the body is highly variable but I just measured one finger to another and it was 5M Ohms. From one hand to the other was about 10M. (1)
With an LM334, it will just max-out to the available voltage and you won't get 1mA.
To push 1mA through 10M requires DANGEROUS VOLTAGES!
1mA through your body won't hurt you, but that variability in resistance means that anything over 50V is considered dangerous by the regulating agencies.
...Normally you need a negative power supply to get negative voltages. But if the load isn't grounded you can use a bridge circuit to reverse the connections. With AC you can use a capacitor and that will take -out the "DC component" for an average voltage of zero. Sometimes that works with a square wave.
(1) I'm surprised there wasn't a bigger difference but it's probably related to the small contact with my meter probes.