 # Notation

The list below describes notation used in this book.

• Vectors: Boldface is used to indicate a vector; e.g., the electric field intensity vector will typically appear as . Quantities not in boldface are scalars. When writing by hand, it is common to write “ ” or “ ” in lieu of “ .”
• Unit vectors: A circumflex is used to indicate a unit vector; i.e., a vector having magnitude equal to one. For example, the unit vector pointing in the direction will be indicated as . In discussion, the quantity “ ” is typically spoken “x hat.”
• Time: The symbol is used to indicate time.
• Position: The symbols , and indicate positions using the Cartesian, cylindrical, and polar coordinate systems, respectively. It is sometimes convenient to express position in a manner which is independent of a coordinate system; in this case, we typically use the symbol . For example, in the Cartesian coordinate system.
• Phasors: A tilde is used to indicate a phasor quantity; e.g., a voltage phasor might be indicated as , and the phasor representation of will be indicated as .
• Curves, surfaces, and volumes: These geometrical entities will usually be indicated in script; e.g., an open surface might be indicated as and the curve bounding this surface might be indicated as . Similarly, the volume enclosed by a closed surface may be indicated as .
• Integrations over curves, surfaces, and volumes will usually be indicated using a single integral sign with the appropriate subscript. For example:

is an integral over the curve

is an integral over the surface

is an integral over the volume

.

• Integrations over closed curves and surfaces will be indicated using a circle superimposed on the integral sign. For example:

is an integral over the closed curve

is an integral over the closed surface

A “closed curve” is one which forms an unbroken loop; e.g., a circle. A “closed surface” is one which encloses a volume with no openings; e.g., a sphere.

• The symbol “ ” means “approximately equal to.” This symbol is used when equality exists, but is not being expressed with exact numerical precision. For example, the ratio of the circumference of a circle to its diameter is , where .
• The symbol “ ” also indicates “approximately equal to,” but in this case the two quantities are unequal even if expressed with exact numerical precision. For example, as a infinite series, but for . Using this approximation , which is in good agreement with the actual value .
• The symbol “ ” indicates “on the order of,” which is a relatively weak statement of equality indicating that the indicated quantity is within a factor of 10 or so the indicated value. For example, for a class of iron alloys, with exact values being being larger or smaller by a factor of 5 or so.
• The symbol “ ” means “is defined as” or “is equal as the result of a definition.”
• Complex numbers: .
• See Appendix C for notation used to identify commonly-used physical constants.

Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 CC BY-SA 4.0 Swipe left and right to change pages. Get the latest tools and tutorials, fresh from the toaster.

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