This book is based upon theoretical, numerical and simulation studies of electrostatic potentials in the presence of low frequency waves in quantum dusty plasmas. Such research have gained considerable attention due to their applications in solid state physics, microelectronics, semiconductor systems, nanotechnologies, metallic nanostructures, nano tubes, and high intense laser-produced plasmas. On the other hand, recently developed quantum plasma models have successfully predicted some new aspects of plasmas in microelectronic devices with nano-electronic components, dense astrophysical systems and also in the laser produced plasmas. Using the quantum hydrodynamic (QHD) model author have investigated shielding/oscillatory potentials of a static/moving test charge in quantum dusty plasmas with the external magnetic field effects.