Electromagnetism

Gradient

Vector that points in the direction of the maximum rate of increase of a scalar field.

Directional Derivative

The rate of change of a function in the direction of a specific unit vector u

Divergence

Measures the "net outflow" or "net outward flux “ of a vector field from a point. Positive = Source; Negative = Sink.

Curl

Measures the rotation or "swirl" or circulation of a vector field or If zero, the field is "Irrotational."

Laplacian

Used in Poisson’s and Laplace’s equations to find potential distributions.

Green’s Theorem

Relates a line integral around a closed plane curve C to a double integral over the plane region bounded by C

Stokes’ Theorem

> It states that the surface integral of the curl of a function over the surface bounded by a closed surface will be equal to the line integral of the particular vector function around it.

> Relates the circulation of a vector field around a closed path to the flux of its curl through any surface bounded by that path.

Gauss Divergence Theorem (Gauss-Ostrogradsky)

> It states that the vector’s outward flux through a closed surface is equal to the volume integral of the divergence over the area within the surface.

> Relates the flux of a vector field through a closed surface to the volume integral of the divergence over the region inside.

Conservative

If the vector field has a vanishing curve (∇XE=0) it s called____

Solenoidal

If the vector field it has a vaishing divergence (∇⋅B=0), it is called ______

scalar or dot product

In a normal (perpendicular) vector, their _____ is zer

Irratational

A vector field with vanishing curl

Scalar, Vector

The Gradient input is ____ and output is _____

Vector, Scalar

The Divergence input is ____ and output is _____

Vector, Vector

The Curl input is ____ and output is _____

Scalar, Scalar

The Laplacian input is ____ and output is _____

Poisson Equation

If the cylindrical coordinate is ∇² ≠0 then it is_____