4: Static and Quasistatic Fields
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- 4.1: Introduction to Static and Quasistatic Fields
- This page discusses static electric and magnetic fields in the context of Maxwell’s equations, focusing on their behavior when time derivatives are absent. It covers the relationships between electric fields and charge distributions, the roles of electric and magnetic potentials, and the derivation of Laplace’s equation under partial charge knowledge. Quasistatic conditions enable simplifications in analyzing field interactions.
- 4.2: Mirror image charges and currents
- This page explains a problem-solving technique using mirror-image charges and currents to simplify complex electromagnetic issues. By introducing a duplicate charge of opposite sign, it demonstrates how to analyze electric fields near a conductive plane without the conductor itself, ensuring perpendicular electric field lines.
- 4.3: Relaxation of Fields and Skin Depth
- This page explains the exponential decay of electric and magnetic fields in conducting media under quasistatic conditions, characterized by specific relaxation times related to material properties. It explores how induced currents affect applications like induction heating and electromagnetic shielding, leading to the derivation of differential equations for current dynamics in cylinder configurations. Additionally, the text addresses transformer core design aimed at reducing eddy current losses.
- 4.4: Static fields in inhomogeneous materials
- This page covers the behavior of static electric and magnetic fields in inhomogeneous materials, focusing on capacitors and conductors. It discusses fundamental laws (Faraday's, Gauss's, and Ampere’s) and relationships in electric displacement and current density, as well as magnetic flux. Key topics include conductivity variations, free surface charges, and the analogies between electric and magnetic circuits, including parameters like resistance and magnetic reluctance.
- 4.5: Laplace’s equation and separation of variables
- This page covers Laplace's equation in static electric and magnetic fields, focusing on solving it via separation of variables in various coordinate systems, including Cartesian, cylindrical, and spherical coordinates. It explores how different boundary conditions lead to unique solutions, using specific examples like conducting cylinders and spheres with sinusoidal voltage distributions.
- 4.6: Flux tubes and field mapping
- This page addresses static field flux tubes, which are collections of electric or magnetic field lines in areas without charge, highlighting principles like zero divergence and curl, and the conservation of flux. It introduces field mapping for visualizing these fields around equipotential surfaces, detailing the creation of these surfaces and field lines, and mentions the role of computer algorithms in facilitating this visualization in both two-dimensional and three-dimensional contexts.
Thumbnail: Electric field lines due to a point charge in the vicinity of PEC regions (shaded) of various shapes. (CC BY SA 4.0; K. Kikkeri).