In silicon clusters a structural transition from prolate to near-spherical structures takes place at a size of about 25-30 atoms. While some of the prolate clusters are very polar, there has been no experimental evidence of the presence of dipole moments in larger silicon clusters with near-spherical shape. By means of electric molecular beam deflection experiments at cryogenic temperatures, it was possible to prove for the first time that SiN clusters with more than N = 30 atoms are also polar. Interestingly, the dipole moment per atom for clusters in the range between 30 and 80 or 90 atoms is almost constant and amounts to 0.02 D. This unusual behaviour manifests in effective polarizabilities increasing linearly with cluster size. The dipolar contribution to the polarizability means that SiN clusters with N = 80 atoms can be polarized more than twice as well as a correspondingly small sphere with the dielectric properties of bulk α-Si. This finding is analysed with quantum chemical calculations concerning the geometric structure as well as the charge distribution and is related to the dielectric behaviour of polar semiconductor nanocrystals.