Electromagnetism Electromagnetism, Second Edition is suitable for a first course in electromagnetism, whilst also covering many topics frequently encountered in later courses. The material has been carefully arranged and allows for flexibility in its use for courses of different length and structure. A knowledge of calculus and an elementary knowledge of vectors is assumed, but the mathematical properties of the differential vector operators are described in sufficient detail for an introductory course, and their physical significance in the context of electromagnetism is emphasised. In this Second Edition the authors give a fuller treatment of circuit analysis and include a discussion of the dispersion of electromagnetic waves. Electromagnetism, Second Edition features: The application of the laws of electromagnetism to practical problems such as the behaviour of antennas, transmission lines and transformers. Sets of problems at the end of each chapter to help student understanding, with hints and solutions to the problems given at the end of the book. Optional “starred” sections containing more specialised and advanced material for the more ambitious reader. An Appendix with a thorough discussion of electromagnetic standards and units. Recommended by many institutions. Electromagnetism. Second Edition has also been adopted by the Open University as the course book for its third level course on electromagnetism. The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw the Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett.

Social Security reform proposals are often presented in terms of their differential impacts on hypothetical or 'example' workers. Our work explores how different benchmarks produce different replacement rate outcomes. We use the Health and Retirement Study (HRS) to evaluate how Social Security benefit replacement rates differ for actual versus hypothetical earner profiles, and we examine whether these findings are sensitive to alternative definitions of replacement rates. We find that workers with the median HRS profile would be estimated to receive benefits worth 55% of lifetime average earnings, versus 48% for the SSA medium scaled profile. Since US policymakers tend to prefer a replacement rate measure tied to workers' own past earnings, using these metrics would yield higher replacement rates compared to commonly used scaled illustrative profiles. However, benchmarks that use population as opposed to individual earnings measures to compare individual worker benefits to pre-retirement consumption produce lower replacement rates for HRS versus hypothetical earners.