You might calibrate by using the traditional gravity experiment.

Rewritten in response to comments.

The torsion balance is often used to measure gravitational attraction of small objects.

You could make a torsion balance with your copper sphere. Add a metal sphere B as shown in the diagram. Calculate the gravitational attraction. Measure the deflection. Use this to calibration your balance.

If gravity is weaker than the forces you are interested in, charge the spheres and calculate the electrostatic attraction/repulsion.