Originally posted by wolram
hi, electromagnetic radiation is a combination of oscillating electric and magnetic fields...if a transmiter sends a cmplex elctro magnetic signal into space and then shuts down, there is no longer a source of information to the signal, how does this oscillating electromagnetic field keep its information?
div B = 0
div E = 0
curl B = 1/c E
t
curl E = -1/c B
t
Maxwell equations are written in many forms. this is one sophomore textbook form of the equations "in free space".
That means no charged objects around and barmagnets and stuff.
E is the electric field, a vector E1,E2,E3 defined at every point x,y,z in space and at every time t.
B is the magnetic field, a vector B1,B2,B3 defined at every point x,y,z in space and at every time t.
E
t is the time-derivative of E----it is also a vector (the change is E) defined at every t,x,y,z
B
t is the time-derivative of B----likewise a vector (the change is B) defined at every t,x,y,z
Intuitively, the RHS time derivatives should be on the left because we want to know how the fields will change in terms of something about them now, in the present moment.
Maxwell says what matters in the present moment (in determining those changes) is the "curls" of E and B.
these are some partials like E2
z and E3
y The E partials in the curl are combined in a way that describes the extent the E field arrows go around in circles or describe eddying motion. Same for the B curl.
Partials like E1
x, E2
y, E3
z don't occur in the curl. They describe the extent to which the field is spreading out or coming together. (As it would at point charges or point "sources".) These terms are combined in the *divergence* terms which Maxwell says are zero in free space.
div E = E1
x+E2
y+E3
z = 0
says that in free space there are no charged particles or other sources from which the field radiates out in all directions.
There is a similar equation for divergence of B = div B.
Convergence is just the negative of divergence. Since the fields have no divergence or convergence, all they can do have the little vectors pointing around in circular eddies---which is estimated by curl E and curl B.
And, by good fortune, curl E and curl B are sufficient to determine the future changes to expect in the field
These will bring about a slightly new terrain of vectors and the new fields of vectors will have slightly new curls, and so it goes.
The curls of today's fields determine the fields of tomorrow.
And there is a lovely reciprocity-----the curl in B determines how E will change----the curl in E determines how B will change.
These are the four Maxwell equations.
Michael Faraday was a practical man who worked with coils and batteries and stuff and did hardware demonstrations and HE began to imagine fields. He thought visually and drew pictures of fields. This is where it began. Maxwell's first paper on electricity, around 1855, was called "On Faraday's Lines of Force."
Maxwell was an intellectual who put facts about fields from Faraday and others into a complete symmetric system of equations which worked together so that undulations could travel in empty space. The field became an independent dynamic entity.
The Britannica calls Maxwell's 1873
Treatise on Electricity and Magnetism "one of the most splendid monuments ever raised by the genius of a single individual."
This may in the end prove a fair assessment and not an overstatement.
