I have an N-channel MOSFET circuit like this, except there is a more detailed (still resistive) load circuit in place of the LED and R1.
I attach my oscilloscope probe to gate (no other connections to gate at that point), and ground to ground. I can see drain-side circuit voltage fluctuations (measured separately) on the scope (low current, low voltage).
I thought the gate was pretty well insulated from the drain side; I don't know but based on my currently limited knowledge of MOSFETs I am wondering if the MOSFET is fried.
Best Answer
You should never leave the gate of a MOSFET floating like that. Static charges can easily puncture the gate oxide, permanently damaging it. Tie a high-value resistor (1 megohm or so) between the gate and the source.
Yes, the gate is very well insulated from the drain/source, but there is a significant amount of capacitive coupling between them, which is probably what you're seeing on your scope.