Inductive charging problem
Short answer: It doesn't work this way. U1*I1 == U2*I2 is only meaningful for the ideal transformer. No losses and a coupling of 100%.

You have neither of these. Because your coils don't share a common iron core, the coupling is in the range of 5% at most and your losses depend on the amount of current you want to transfer through this loose coupling.

You have to reduce the air gap for a tighter coupling and will see the amount of current you can draw from the secondary without a loss in voltage increases greatly.