Pickup Signal from a Wire - without a physical connection
With a capacitive pickup from a short length of wire running along (parallel to, or wrapped around) your "wire under test," you're going to receive a (very) high-impedance signal pickup.

In order to get good amplification of this high-impedance signal, you're going to need to use a higher input impedance amplifier.

Here's a diagram of one such amp (using a J211 JFET transistor) I was working on for another question (modified for your 10khz source frequency):