Field in physics means a region where every position is tied to a value, which can be either scalar or vector. Vector fields apply many concepts, ideas, and computations from multivariable calculus, since if we plot a field in a Cartesian coordinate system, the magnitude and directions of vectors are dependent on its corresponding x, y coordinates, and we are often interested in investigating in these relationships or trends of changing.
Vector field is not unexpectedly helpful for modeling electric field, which is defined by force (a vector variable) applied to charged particles occupying any location in the field. Electric field intensity describes the force exerted on every unit charge. Plotting a vector field diagram from Coulomb’s Law – the formula that evaluates electric force – denotes the forces applied to a unit charge at each position. Physical meaning of other calculus calculations, e.g. flux, curl, linear integral, can also be defined.
