He received his bachelor's degree from Union College in 1962 and his Ph.D. in physics from Johns Hopkins University in 1966. He served on the faculty of the University of Iowa before joining the University of Wisconsin in 1981, where he held the title of Irving Langmuir Professor of Engineering Physics. Noah was a fellow of the American Physical Society (APS), American Vacuum Society, Institute of Physics, and the IEEE. In 2004, he received the James Clerk Maxwell Prize for Plasma Physics from the APS, and in 2015 the Marie Sklodowska-Curie Award from IEEE. He was the founding Editor-in-Chief of the influential journal Plasma Sources Science and Technology. He was a strong presence and force in the Gaseous Electronics Conference and the American Vacuum Society.

Noah was a key architect in shaping the modern field of experimental low temperature plasmas. His most notable contributions center on his investigations of plasma sheaths and the measurement tools that he pioneered for their study including a variety of electrostatic probe methods. He used these tools to glean profound insight and understanding of the complexities of plasma sheaths, solitons, and double layers. Noah's name is almost synonymous with the emissive probe, a powerful tool to study the electrical potentials within plasma sheaths. Noah perfected the inflection method to study plasmas in diverse environments ranging from thrusters to semiconductor processing. He developed many other methods and tools to investigate plasmas that are now standards in the field, from probes to laser induced fluorescence. His seminal paper “Sheaths: More Complicated Than You Think”, which was published in Physics of Plasmas, has become a classic and should be required reading for new entries to the field.

Noah was also known for deftly using multipole plasma sources to investigate the intricacies of plasma transport. These studies yielded great insight into the puzzling questions of plasma leaking through magnetic cusps. Noah's advances in understanding these complex transport processes enabled optimizing the efficiency and stability of multipole ion sources such as gridded ion thrusters for spacecraft. He also developed plasma sources for specific applications such as the helicon and rf plasma cathode sources for semiconductor manufacturing applications and space propulsion. Noah was a great mentor to many, having supervised more than fifty-five students to their Ph.D. degrees.

He was also the Director of the Center for Plasma-Aided Manufacturing. The Center provided important input to industry on industrial applications of plasmas in areas such as plasma etching for the semiconductor industry.