electromagnetismo: teoría de campos

E(x,y,z) = kq·< f(x),f(y),f(z) >

¬E(x,y,z) = kq·< g(y,z),g(z,x),g(x,y) >

div[ E(x,y,z) ] = d_{x}[f(x)]+d_{y}[f(y)]+d_{z}[f(z)]

d_{xyz}^{3}[ Flux[ E(x,y,z) ] ] = d_{x}[f(x)]+d_{y}[f(y)]+d_{z}[f(z)]

div[ ¬E(x,y,z) ] = 0

d_{xyz}^{3}[ Flux[ ¬E(x,y,z) ] ] = 0

 

rot[ E(x,y,z) ] = kq·< x·( f(y)+(-1)·f(z) ),y·( f(z)+(-1)·f(x) ),z·( f(x)+(-1)·f(y) ) >

rot[ ¬E(x,y,z) ] = kq·< x·( g(z,x)+(-1)·g(x,y) ),y·( g(x,y)+(-1)·g(y,z) ),z·( g(y,z)+(-1)·g(z,x) ) >

flux[ rot[ E(x,y,z) ] ] = 0

flux[ rot[ ¬E(x,y,z) ] ] = ...

... x·( int[ g(y,z) ] d[y]·z+(-1)·int[ g(y,z) ] d[z]·y )+...

... y·( int[ g(z,x) ] d[z]·x+(-1)·int[ g(z,x) ] d[x]·z )+...

... z·( int[ g(x,y) ] d[x]·y+(-1)·int[ g(x,y) ] d[y]·x )

d_{t}[ E(x,y,z) ] = ...

... kq·< d_{x}[f(x)]·d_{t}[x], d_{y}[f(y)]·d_{t}[y],d_{z}[f(z)]·d_{t}[z] >

J(x,y,z) = d_{t}[ E(x,y,z) ]+rot[ E(x,y,z) ]

d_{t}[ ¬E(x,y,z) ] = ...

... kq· ...

... < ...

... int[ d_{yz}^{2}[g(y,z)]·d_{t}[y]·d_{t}[z] ] d[t], ...

... int[ d_{zx}^{2}[g(z,x)]·d_{t}[z]·d_{t}[x] ] d[t], ...

... int[ d_{xy}^{2}[g(x,y)]·d_{t}[x]·d_{t}[y] ] d[t] ...

... >

¬J(x,y,z) = d_{t}[ ¬E(x,y,z) ]+rot[ ¬E(x,y,z) ]

E(x,y,z) = ...

... kq·< f(x),f(y),f(z) >

¬E(x,y,z) = ...

... (1/2)·kq·< f(y)+f(z),f(z)+f(x),f(x)+f(y) >

E(x,y,z) = ...

... kq·< e^{f(x)},e^{f(y)},e^{f(z)} >

¬E(x,y,z) = ...

... kq·< e^{( f(y)+f(z) )},e^{( f(z)+f(x) )},e^{( f(x)+f(y) )} >