Maxwell I: Fundamentals

Purpose

We provide the mathematical and physical framework for equations, ultimately formulated by Maxwell, that form the basis for EM surveys.

Background about the individual laws, their discoverers, and associated physical principles are first provided first in Formative Laws. The first order equations are then combined to generate the formative Maxwell Equations in the time and frequency domains. These equations can be solved once sources are specified and appropriate boundary and interface conditions are provided. Much can be learned by solving the equations in an unbounded homogeneous earth, with plane wave and dipolar sources. We present these along with software apps that allow the user to visualize the fields and fluxes and explore the relationships between physical properties, sources and EM fields. These examples also allow us to introduce concepts, terminology and background mathematics that are used throughout EM.geosci. For the user who is already familiar with basics of EM, the starting point might be the synopsis of the Maxwell’s equations presented in the Quick- Guide. In general, physical properties vary in 3D and sources have many geometries. Different approaches to solving Maxwell’s equations may be required and we outline some principles for helping the user decide which route to take and how to proceed.

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