Measurement of electrostatic induction

How is it with the electrostatic induction measurement? Everywhere you can read about the effect of electrostatic induction but I still can’t found any detailed explanations or quantitative measurements. Perhaps someone here might help me.

Here is a Picture about the effect I am refering to:

The process is realy simple. In the last picture the sphere is charged (one positive, one negative). But how high is the amount of electric charge? One can break this down to a more simple experiment: I have a capasitor which generates an electric field. I can calculate the homogeneously electric field by the voltage and dimension of the capacitor. Now I am moving two connected plates into this field, disconnect them and put them out of the field. One plate is charged positive, one negative. But how high is the amount of electric charge in dependence of the electric field?

I thought it might work by calculating the Electric displacement field? But I am willing to see Solutions by other People.
Is it calculated this way or is there another method?

Thanks to all of you and have a nice day. 🙂