Floating Conductor Next to AC Power Source

Let's say I have a conductive metal sphere connected to a 50Hz 1kVrms AC Power Source referenced to Earth ground. About 3cm away, there's an identical metal sphere suspended by a non-conductive material. Does the floating conductor gain a charge from an electric field from the source? What is it's approximate voltage against ground?

• we need to know the size of the sphere. And how far away to GND. You have a capacitive voltage divider. – analogsystemsrf Oct 25 '19 at 17:11

$$V_{floating}=V_{source}*\frac{C_1}{C_1+C_2}$$ where C1 is the capacitance between the two spheres and C2 is the capacitance between the floating sphere and Earth. This equation works for both AC and DC voltage values.