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Tailored electrostatic potentials are at the heart of semiconductor nanostructures. We present measurements of size and screening effects of the tip-induced potential in scanning gate microscopy on a two-dimensional electron gas. First, we show methods on how to estimate the size of the tip-induced potential. Second, a ballistic cavity is studied as a function of the bias-voltage of the metallic top gates and probed with the tip-induced potential. It is shown how the potential of the cavity changes by tuning the system to a regime where conductance quantization in the constrictions formed by the tip and the top gates occurs. This conductance quantization leads to a unprecedented rich fringe pattern over the entire structure. Third, the effect of electrostatic screening of the metallic top gates is discussed.