§16§This book is an original study aimed at understanding how vacuum magnetic fields change with time. Specifically, it describes the waves that radiate from a sphere when the electric current on its surface is turned on or off, either suddenly, gradually, or periodically.§Numerical simulations are an invaluable source of information about this and related subjects, but they are often more difficult to interpret than exact, closed-form solutions that can easily be applied to a variety of situations. Thus, the objective here is to obtain an exact solution of Maxwell's equations in closed form-something simple, yet rigorous, which can be used as a model for understanding transient magnetic fields in more complicated situations. The work therefore stands as a self-contained solution of Maxwell's equations for an electric current wrapped around the surface of a sphere.§This study assumes a strong background in electromagnetism or a relatedresearch area. Online animations are availab §16§le for each figure to better illustrate the motions of magnetic field lines. §04§Preface.- Chapter 1: Introduction.- Chapter 2: The Vector Potential For a Current Step.- Chapter 3: Fields and Field Lines.- Chapter 4: Radiated Energy and the Sudden Turnoff.- Chapter 5: The Fields of a Linear Current Ramp.- Chapter 6: The Stretching and Pinchoff of Loops.- Chapter 7: Non-Linear Current Ramps.- Chapter 8: Other Examples of interacting Fields.- Chapter 9: Short-Wave Radiation.- Chapter 10: Radiated Energy for General Current Ramps.- Chapter 11: Oscillating Currents.- Chapter 12: Single-Source Dynamics.- Chapter 13: The Interaction of Two Sources.- Chapter 14: Concentric Sources.- Chapter 15: The Boundary-Value Approach.- Chapter 16: The Conducting Core.- Chapter 17: Summary.- Chapter 18: Epilogue.- Index. §13§"This book is a comprehensive report from the author's theoretical investigations on transient magnetic fields ... . All necessary calculations have been done analytically and presented in a very accessible manner, enabling the reader to follow them with ease. ... The book has been carefully edited. It includes many color drawings showing the calculated magnetic field configurations." (Radoslaw Szmytkowski, zbMATH 1479.78002, 2022) §02§at the Lunar and Planetary Laboratory of the University of Arizona (LPL/ UA).§
