Vectors
The cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a threedimensional oriented Euclidean vector space is denoted by the symbol X.
Given two linearly independent vectors a and b, the cross product, a × b (read “a cross b”), is a vector that is perpendicular to both a and b,^{[1]} and thus normal to the plane containing them.
https://en.wikipedia.org/wiki/Cross_product
The exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higherdimensional analogues. The exterior product of two vectors u and v denoted by
is called a bivector and lives in a space called the exterior square, a vector space that is distinct from the original
space of vectors. The magnitude^{[4]} of can be interpreted as the area of the parallelogram with sides u and v which in three dimensions can also be computed using the cross product of the two vectors.
https://en.wikipedia.org/wiki/Exterior_algebra#Inner_product
An eigenvector (/ˈaɪɡənˌvɛktər/) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled.
In rotational motion of a rigid body, the principal axes are the eigenvectors of the inertia matrix.
real symmetric matrices have real eigenvalues.
If A is an n × n matrix, then the sum of the n eigenvalues of A is the trace of A and the product of the n eigenvalues is the determinant of A.
Tensors:
A tensor is an ndimensional array satisfying a particular transformation law.
Not every Matrix is a rank 2 Tensor.
A Rank 2 tensor can be represented as a matrix of numbers — in conjunction with an associated transformation law.
A Rank 3 tensor can be represented as a 3dimensional array of numbers — in conjunction with an associated transformation law.
Rank 3 example: LeviCivita_symbol
https://en.wikipedia.org/wiki/LeviCivita_symbol
Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).
A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). https://rinterested.github.io/statistics/tensors2.html 

E is the electric vector
B is the magnetic induction
ρ is the electric charge density
j is the electric current density
ε0 is the permittivity of free space
ε is the dielectric constant (or permittivity)
c is the speed of light
σ is the specific conductivity
μ is the magnetic permeability
j=σE
D=εE D is the electric displacement
B=μH H is the magnetic vector
Maxwell Equations
Gauss’s law
Divergence of electric field is proportional to the the volume charge density
is the outward pointing unit normal at each point on every on the boundary of surface S of Volume V
Gauss’s law for magnetism
The magnetic field B has divergence equal to zero. It is equivalent to the statement that magnetic monopoles do not exist.
Faraday’s law of induction
A circulating electric field is produced by a magnetic field that changes with time.
AmpereMaxwell Law
A circulating magnetic field is produced by an electric current and by an electric field that changes with time.
Deriving Electromagnetic waves from Maxwell’s equations https://www.youtube.com/watch?v=LsXjVfucHU
https://web.mit.edu/sahughes/www/8.022/lec20.pdf
https://en.wikipedia.org/wiki/Displacement_current
https://physics.stackexchange.com/questions/166888/thepropagationofelectricfield
Book: https://matterandinteractions.org/
Liénard–Wiechert potential classical electromagnetic effect of a moving electric point charge
What is the proof of the BiotSavart law from Maxwell equations
https://www.khanacademy.org/science/ininclass12thphysicsindia/movingchargesandmagnetism
Magnetic field of a moving charge
میدان و امواج
Feynman
Full https://www.youtube.com/watch?v=kExgRfuhhk
Richard P Feynman: Quantum Mechanical View of Reality – YouTube
QED:New Queries (Richard Feynman 4/4) – YouTube
QED: Electrons and their Interactions (Richard Feynman 3/4) – YouTube
Explanations
This relates to electric field in that the charge moving through a circuit to light a light bulb has to be driven by some electric field, so you can reasonably ask how that field is established, and how much time it takes. Qualitatively, the necessary field is established by excess charge on the surface of the wires, with the surface charge being generally positive near the positive terminal of a battery and generally negative near the negative terminal, and dropping off smoothly from one to the other so that the electric field is more or less piecewise constant (that is, the field is the same everywhere inside a wire, and the field is the same everywhere inside a resistor, but the two field values are not the same).
When the circuit is first connected, there is a rapid redistribution of the charge on the surface of the wires which establishes the surface charge gradients that drive the steadystate current that will eventually do whatever it is you want it to do. The time required to establish the gradients and settle in to the steadystate condition is very fast, most likely on the order of nanoseconds for a normal circuit.