Question

the geometry of electromagnetic feild is?​

Answer 1

Answer:

plz mark as BRAINLIEST plz

Explanation:

We have now enough background to specify a proper

meaning for term “geometry of electromagnetism”. The

key idea is: electromagnetic fields can be interpreted as an-

other collection of charts mapping to set X. To explain the

idea, notice first that we know already that {X, G} is a Rie-

mannian manifold; Locally every tangent space of x ∈ X

has the Euclidean structure.

Now, let us employ electrostatics as a simplifying ex-

ample and say c is a topologically trivial charged conduc-

tor. The electrostatic field is the pair {e, d}, where e is the

1-form called electric field and d the 2-form called elec-

tric flux. Thanks to the properties of manifold {X, G}, in

the complement of c in X we may say what pair {e, d} is

precisely: Assuming appropriate boundary conditions pair

{e, d} is the solution of equations

de = 0 , (1)

dd = 0 , (2)

d = e (3)

where d is the exterior derivative and is the Hodge oper-

ator including permittivity. Notice, although we do not se-

lect explicitly some coordinate system, the pair {e, d} ful-

filling (1), (2), and (3) is already fully meaningfull.

As soon as we may talk of the electrostatic field {e, d},

we may also define equipotential layers and field lines:

Definition 1: A 2-dimensional connected submanifold S

of M = {X, G} is an equipotential layer, if for all x ∈ S

and v ∈ TxS (i.e, vector v is in the tangent space of S at

point x) implies ex(v)=0.

Proceedings of ICAP 2006, Chamonix, France MOA1MP02

Numerical Methods in Field Computation