Vector Analysis and Physical Quantities

Flashcards covering key definitions and concepts from the lecture on Vector Analysis, Physical Quantities, Units, Scalars, and Vectors.

Vector Analysis

The branch of mathematics developed to describe quantities that are both directional in nature and distributed over regions of space, best suited for electromagnetics.

Physical Quantities

Entities that can be perceived and measured.

Operational Definition

The definition of a physical quantity in terms of the measurement procedure used to measure it.

Units

Standards used as a comparison for what is being measured.

Fundamental Quantities

Sets of quantities, by convention, regarded as primary and specified in internationally accepted fundamental units.

MKSA System

A widely accepted unit system whose fundamental quantities are length, mass, time, and current, specified in meters, kilograms, seconds, and amperes, respectively.

Derived Units

Units that are specified in terms of the fundamental units, e.g., the Newton ([kg m/sec²]).

Dimensions of a Physical Quantity

Specified by the powers of the fundamental physical quantities that occur in its definition.

Discrete Quantities

Physical quantities defined over regions of space or at single points, but not on a point-by-point basis throughout a region.

Field Quantities

Physical quantities defined on a point-by-point basis throughout a region of space (e.g., temperature in a room).

Scalar

A quantity that can be specified by a single number and its associated unit (e.g., temperature, altitude, weight).

Vector

A quantity that can be specified by both a magnitude and a direction (e.g., velocity, force).

Magnitude of a Vector

A positive-valued scalar that includes its associated unit, represented as |A| or A.

Direction of a Vector

A spatial orientation of a vector.

Discrete Vector

A vector associated with regions of space but not a specific point, whose representation can be translated freely.

Directed Distance Rab

A discrete vector whose magnitude equals the distance between points a and b, and whose direction is parallel to the line directed from a to b.

Quiver Plot (Needle Plot)

A graphical representation of a vector field at equally spaced points, conveying both the magnitude and direction of the vector.

Streamline Plot

A graphical representation using continuous lines tangent to the vector's direction at each point, best for conveying the sense of a vector's 'flow'.

Vector Addition and Subtraction

Operations defining the sum of two vectors A and B as a vector completing the parallelogram formed by A and B, or using the tail-to-head rule.