Recent ammonia (1,1) inversion line data on the Galactic star forming region Sgr B2 show that the column density is consistent with a radial Gaussian density profile with a standard deviation of 2.75 pc. Deriving a formula for the virial mass of spherical Gaussian clouds, we obtain M_vir =1.9 * 106 Mo for Sgr B2. For this matter distribution, a reasonable magnetic field and an impinging flux of cosmic rays of solar neighbourhood intensity, we predict the expected synchrotron emission from the Sgr B2 giant molecular cloud due to secondary electrons and positrons resulting from cosmic ray interactions, including effects of losses due to pion production collisions during diffusive propagation into the cloud complex. We assemble radio continuum data at frequencies between 330 MHz and 230 GHz. From the spectral energy distribution the emission appears to be thermal at all frequencies. Before using these data to constrain the predicted synchrotron flux, we first model the spectrum as free-free emission from the known ultra compact H ii regions plus emission from an envelope or wind with a radial density gradient, and obtain an excellent fit. We thus find the spectrum at all frequencies to be dominated by thermal emission, and this severely constrains the possible synchrotron emission by secondary electrons to quite low flux levels. The absence of a significant contribution by secondary electrons is almost certainly due to multi-GeV energy cosmic rays being unable to penetrate far into giant molecular clouds. This would also explain why 100 MeV-GeV gamma-rays (from neutral pion decay or bremsstrahlung by secondary electrons) were not observed from Sgr B2 by EGRET, while TeV energy gamma-rays were observed, being produced by higher energy cosmic rays which more readily penetrate giant molecular clouds.