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) )} >

rotacional vectorial

x·( f(y)+(-1)f(z) )
y·( f(z)+(-1)f(x) )
z·( f(x)+(-1)f(y) )

bi-motor eléctric

(x+y)^{2} = x^{2}+2xy+y^{2}


Bobines:
E_{1,x} = < E·cos(st),0,0 >
E_{1,y} = < 0,E·sin(st),0 >
E_{2,x} = < E·cos(st),0,0 >
E_{2,y} = < 0,E·sin(st),0 >


d_{t}[E_{1,x}][o]d_{t}[E_{2,x}]+d_{t}[E_{1,y}][o]d_{t}[E_{2,y}] = E·s^{2}


Bobines:
E_{1,x} = < E·cos((-s)t),0,0 >
E_{1,y} = < 0,E·sin((-s)t),0 >
E_{2,x} = < E·cos((-s)t),0,0 >
E_{2,y} = < 0,E·sin((-s)t),0 >


d_{t}[E_{1,x}][o]d_{t}[E_{2,x}]+d_{t}[E_{1,y}][o]d_{t}[E_{2,y}] = E·s^{2}


Bobines:
E_{1,x} = < E·cos(st),0,0 >
E_{1,y} = < 0,E·sin(st),0 >
E_{2,x} = < E·cos((-s)t),0,0 >
E_{2,y} = < 0,E·sin((-s)t),0 >


d_{t}[E_{1,x}][o]d_{t}[E_{2,x}]+d_{t}[E_{1,y}][o]d_{t}[E_{2,y}] = (-1)·E·s^{2}


Bobines:
E_{1,x} = < E·cos((-s)t),0,0 >
E_{1,y} = < 0,E·sin((-s)t),0 >
E_{2,x} = < E·cos(st),0,0 >
E_{2,y} = < 0,E·sin(st),0 >


d_{t}[E_{1,x}][o]d_{t}[E_{2,x}]+d_{t}[E_{1,y}][o]d_{t}[E_{2,y}] = (-1)·E·s^{2}

vectors corrent-rotacionals de camps de variables separades

d_{t}[ F(x,y,z) ] = rot[ E(x,y,z) ]

F(x,y,z) = kq·(1/2)·( x_{k} )^{2} [o(t)o] ( x_{k} )^{[o(t)o](-1)} [o(t)o] ...
... ( ∫ [ f(y_{i}) ] d[t] + (-1)·∫ [ f(z_{j}) ] d[t] ).

d_{t}[ D(x,y,z) ] = rot[ B(x,y,z) ]

D(x,y,z) = (-1)·kq·(1/2)·( x_{k} )^{2} [o(t)o] ( x_{k} )^{[o(t)o](-1)} [o(t)o] ...
... ( ∫ [ f( d_{t}[y_{i}]·t ) ] d[t] + (-1)·∫ [ f( d_{t}[z_{j}]·t ) ] d[t] ).

div[ F(x,y,z) ] = kq·∑ ( x_{k}/d_{t}[x_{k}] )·( f(y_{i})+(-1)·f(z_{j}) ).

div[ D(x,y,z) ] = (-1)·kq·∑ ( x_{k}/d_{t}[x_{k}] )·( f( d_{t}[y_{i}]·t )+(-1)·f( d_{t}[z_{j}]·t ) ).

∯ [ F(x,y,z) ] d[(yz,zx,xy)] = ...

... kq·∑ ( x_{k} )^{2} [o(t)o] ( x_{k} )^{[o(x)o](-1)} [o(t)o] ... 

... ( ∫ [ ∫ [ f(y_{i}) ] d[t] ] d[y_{i}]·z_{j} + (-1)·∫ [ ∫ [ f(z_{j}) ] d[t] ] d[z_{j}]·y_{i} ).

∯ [ D(x,y,z) ] d[(yz,zx,xy)] = ...

... (-1)·kq·∑ ( x_{k} )^{2} [o(t)o] ( x_{k} )^{[o(x)o](-1)} [o(t)o] ... 

... ( ∫ [ ∫ [ f( d_{t}[y_{i}]·t ) ] d[t] ] d[y_{i}]·z_{j} + (-1)·∫ [ ∫ [ f( d_{t}[z_{j}]·t ) ] d[t] ] d[z_{j}]·y_{i} ).

m·d_{tt}^{2}[x_{k}] = p( F(x,y,z)+D(x,y,z) )

x_{k} = V_{k}·t

vectors corrent de camps de variables separades

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

J(x,y,z) = ...

... kq·( d_{t}[f(x_{k})]+(x_{k})·( f(y_{i})+(-1)·f(z_{j}) ) ).

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

... (-1)·kq·( d_{t}[f( d_{t}[x_{k}]·t )]+(x_{k})·( f( d_{t}[y_{i}]·t )+(-1)·f( d_{t}[z_{j}]·t ) ) ).

∯ [ J(x,y,z) ] d[(yz,zx,xy)] = ...
... n·kq·∑ ( (1/(ct)^{n})·( x_{k} )^{(n+(-1))}·d_{t}[x_{k}] + ...
... (-1)·(c/(ct)^{(n+1)})·( x_{k} )^{n} )·(y_{i}z_{j})

∯ [ H(x,y,z) ] d[(yz,zx,xy)] = ...
... (-1)·n·kq·∑ ( (1/(ct)^{n})·( d_{t}[x_{k}]·t )^{(n+(-1))}·( d_{tt}^{2}[x_{k}]·t+d_{t}[x_{k}] ) +...
... (-1)·(c/(ct)^{(n+1)})·( d_{t}[x_{k}]·t )^{n} )·(y_{i}z_{j})

div[ J(x,y,z) ] = kq·∑ d_{tt}^{2}[ f(x_{k}) ]·( 1/d_{t}[x_{k}] )

div[ H(x,y,z) ] = (-1)·kq·∑ d_{tt}^{2}[ f( d_{t}[x_{k}]·t ) ]·( 1/d_{t}[x_{k}] )

m·d_{tt}^{2}[x_{k}] = p( J(x,y,z)+H(x,y,z) )

x_{k} = V_{k}·t

ecuacions de camps

∯ [ E(x,y,z) ] d[(yz,zx,xy)] = Q(x,y,z)
∯ [ B(x,y,z) ] d[(yz,zx,xy)] = A(x,y,z)

∯ [ E(x,y,z) ] d[(yz,zx,xy)] = ∭ [ div[ E(x,y,z) ] ] d[x]d[y]d[z]
∯ [ B(x,y,z) ] d[(yz,zx,xy)] = ∭ [ div[ B(x,y,z) ] ] d[x]d[y]d[z]

div[ E(x,y,z) ] = d_{xyz}^{3}[ Q(x,y,z) ]
div[ B(x,y,z) ] = d_{xyz}^{3}[ A(x,y,z) ]

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

∯ [ d_{t}[ E(x,y,z) ] ] d[(yz,zx,xy)] = ∯ [ J(x,y,z) ] d[(yz,zx,xy)]
∯ [ d_{t}[ B(x,y,z) ] ] d[(yz,zx,xy)] = ∯ [ H(x,y,z) ] d[(yz,zx,xy)]

div[ d_{t}[ E(x,y,z) ] ] = div[ J(x,y,z) ]
div[ d_{t}[ B(x,y,z) ] ] = div[ H(x,y,z) ]

rot[ E(x,y,z) ] = d_{t}[ F(x,y,z) ]
rot[ B(x,y,z) ] = d_{t}[ D(x,y,z) ]

∯ [ F(x,y,z) ] d[(yz,zx,xy)] = G(x,y,z)
∯ [ D(x,y,z) ] d[(yz,zx,xy)] = S(x,y,z)

∯ [ F(x,y,z) ] d[(yz,zx,xy)] = ∭ [ div[ F(x,y,z) ] ] d[x]d[y]d[z]
∯ [ D(x,y,z) ] d[(yz,zx,xy)] = ∭ [ div[ D(x,y,z) ] ] d[x]d[y]d[z]

div[ F(x,y,z) ] = d_{xyz}^{3}[ G(x,y,z) ]

div[ D(x,y,z) ] = d_{xyz}^{3}[ S(x,y,z) ]

Ecuacions d'ona electro-magnétiques y gravito-magnétiques:

d_{t}[ div[ E(x,y,z)+B(x,y,z) ] ] = Lap[ E(x,y,z)+B(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])

d_{t}[ div[ J(x,y,z)+H(x,y,z) ] ] = Lap[ J(x,y,z)+H(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])

d_{t}[ div[ F(x,y,z)+D(x,y,z) ] ] = Lap[ F(x,y,z)+D(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])

d_{tt}^{2}[ E(x,y,z)+B(x,y,z) ] = Lap[ E(x,y,z)+B(x,y,z) ] [o] (d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2})

d_{tt}^{2}[ J(x,y,z)+H(x,y,z) ] = Lap[ J(x,y,z)+H(x,y,z) ] [o] (d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2})

d_{tt}^{2}[ F(x,y,z)+D(x,y,z) ] = Lap[ F(x,y,z)+D(x,y,z) ] [o] (d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2})

lagranià magnétic eléctric

d_{tt}[r] =  ( d_{t}[r]^{n}/r^{n} )


r(t) = t^{(2+(-n))}


d_{tt}[r] = t^{(-n)}


d_{t}[r(t)]^{n} = t^{n(1+(-n))}


( r(t) )^{(-n)}= t^{(2(-n)+n^{2})}

lagranià eléctric

d_{tt}[r] =  ( 1/r^{n} )


r(t) =  t^{( 2/(1+n) )}


d_{tt}[r] = a^{(-2)n/(n+1)}·t^{( ((-2)n)/(1+n) )}

lagranià para-magnétic eléctric

d_{tt}^{2}[x]= ( d_{t}[x]^{n} )


d_{tt}[x(t)] = a^{(1/2)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4)} )^{n/(1+(-n))}·a^{(-1)(1+(-n))/2)} = 1


( x(t) )^{n} = a^{(n/2)+(-1)(n^{2}/4)}·...
... ( a^{(-1)(1+(-n))(2+(-n))/4} )^{n/(1+(-n))} = 1


( x(t) ) = a^{(1/2)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4} )^{(2+(-n))/(1+(-n))}·t^{( (2+(-n))/(1+(-n)) )}


d_{tt}[x(t)] = a^{(1/4)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4) )^{n/(1+(-n))}·a^{(-1)(1+(-n))/2)} = a^{(-1)(1/4)}


( x(t) )^{n} = a^{(n/4)+(-1)(n^{2}/4)}·...
... ( a^{(-1)(1+(-n))(2+(-n))/4} )^{n/(1+(-n))} = a^{(-1)(n/4)}


( x(t) ) = a^{(-1)(1/4)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4} )^{(2+(-n))/(1+(-n))}·t^{(2+(-n))/(1+(-n))}


d_{tt}^{2}[x]= ( a^{(n+(-1))(1/4))}·d_{t}[x]^{n}/c^{n} )
m·d_{tt}^{2}[x]= (k_{e}·pq)·d_{t}[x]^{n}/c^{n} )


a^{(n+(-1))(1/4))} = ( (k_{e}·pq)/(mc^{n}) )


a = ( (k_{e}·pq)/(mc^{n}) )^{( 1/(n+(-1))(1/4)) )}

lagranià para-eléctric

d_{tt}^{2}[x]= ( x^{n}/t^{n} )


d_{tt}[x(t)] = a^{(1/2)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4)} )^{n/(1+(-n))}·a^{(-1)(1+(-n))/2)} = 1


( x(t) )^{n} = a^{(n/2)+(-1)(n^{2}/4)}·...
... ( a^{(-1)(1+(-n))(2+(-n))/4} )^{n/(1+(-n))} = 1


( x(t) ) = a^{(1/2)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4} )^{(2+(-n))/(1+(-n))}·t^{(2+(-n))/(1+(-n))}


d_{tt}[x(t)] = a^{(1/4)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4) )^{n/(1+(-n))}·a^{(-1)(1+(-n))/2)} = a^{(-1)(1/4)}


( x(t) )^{n} = a^{(n/4)+(-1)(n^{2}/4)}·...
... ( a^{(-1)(1+(-n))(2+(-n))/4} )^{n/(1+(-n))} = a^{(-1)(n/4)}


( x(t) ) = a^{(-1)(1/4)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4} )^{(2+(-n))/(1+(-n))}·t^{(2+(-n))/(1+(-n))}


d_{tt}^{2}[x]= ( a^{(n+(-1))(1/4))}·x^{n}/t^{n} )
m·d_{tt}^{2}[x]= (k_{e}·pq)·x^{n}/(ct)^{n} )


a^{(n+(-1))(1/4))} = ( (k_{e}·pq)/(mc^{n}) )


a = ( (k_{e}·pq)/(mc^{n}) )^{( 1/(n+(-1))(1/4)) )}

ones para-electro-magnétiques y para-gravito-magnétiques

m·d_{tt}^{2}[x] = k·pq·( x^{n}/(ct)^{n} )+(-1)·kpq·( d_{t}[x]^{n}/c^{n} )
m·d_{tt}^{2}[x] = k·pq·( x^{n}/(ct)^{n} )+(-1)·kpq·( (d_{t}[x]^{n}·t^{n})/(ct)^{n} )


x(t) = vt


m·d_{tt}^{2}[x] = p·P[E]_{e}(x)+p·P[B]_{e}(x)


d_{tt}[ P[E]_{e}(x)+P[B]_{e}(x) ] = d_{xx}[ P[E]_{e}(x)+P[B]_{e}(x) ]·d_{t}[x]^{2}
d_{tt}[ P[E]_{e}(y)+P[B]_{e}(y) ] = d_{yy}[ P[E]_{e}(y)+P[B]_{e}(y) ]·d_{t}[y]^{2}
d_{tt}[ P[E]_{e}(z)+P[B]_{e}(z) ] = d_{zz}[ P[E]_{e}(z)+P[B]_{e}(z) ]·d_{t}[z]^{2}

para-magnetisme eléctric y para-magnetisme gravitatori

camp para-mangétic eléctric:
B_{e}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) = ...
... (-1)·kq·< (d_{t}[x]·t)^{n}/(ct)^{n} , (d_{t}[y]·t)^{n}/(ct)^{n} , (d_{t}[z]·t)^{n}/(ct)^{n} >


flux[ B_{e}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...
... (-1)·kq·(1/(ct)^{n})·A[n]-[ (x_{i})^{(-1)} ](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t)·xyz


div[ B_{e}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...
... (-1)·n·kq·( ...
... (1/(ct)^{n})·A[n+(-1)](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) + ...
... (-1)(c/(ct)^{n+1}A[n]-[ d_{t}[x_{i}]^{(-1)} ](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t)) ...
... )


camp para-mangétic gravitatori:
B_{g}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) = ...
... kq·< (d_{t}[x]·t)^{n}/(ct)^{n} , (d_{t}[y]·t)^{n}/(ct)^{n} , (d_{t}[z]·t)^{n}/(ct)^{n} >


flux[ B_{g}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...
... kq·(1/(ct)^{n})·A[n]-[ (x_{i})^{(-1)} ](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t)·xyz


div[ B_{g}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...
... n·kq·( ...
... (1/(ct)^{n})·A[n+(-1)](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) + ...
... (-1)(c/(ct)^{n+1}A[n]-[ d_{t}[x_{i}]^{(-1)} ](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ...
... )

potencial para-eléctric y para-gravitatori

potencial eléctric:
E_{e}(x,y,z) = kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >
V_{e}(x,y,z) = ( 1/(n+1) )·kq·(ct)·Q[n+1](x,y,z)
E_{e}(x,y,z) = grad[ V_{e}(x,y,z) ]


flux[ ∫ [ grad[ V_{e}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ( 1/(n+1) )·kq·Q[n](x,y,z)·xyz
div[ ∫ [ E_{e}(x,y,z) ]·< d[x],d[y],d[z]> ] = kq·Q[n](x,y,z)


potencial gravitatori:
E_{g}(x,y,z) = (-1)·kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >
V_{g}(x,y,z) = (-1)·( 1/(n+1) )·kq·(ct)·Q[n+1](x,y,z)
E_{g}(x,y,z) = grad[ V_{e}(x,y,z) ]


flux[ ∫ [ grad[ V_{g}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = (-1)·( 1/(n+1) )·kq·Q[n](x,y,z)·xyz
div[ ∫ [ E_{g}(x,y,z) ]·< d[x],d[y],d[z]> ] = (-1)·kq·Q[n](x,y,z)


ecuacions de camp:
flux[ ∫ [ grad[ V_{e}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ∭ [ div[ ∫ [ E_{e}(x,y,z) ]·< d[x],d[y],d[z]> ] ] d[x]d[y]d[z]
flux[ ∫ [ grad[ V_{g}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ∭ [ div[ ∫ [ E_{g}(x,y,z) ]·< d[x],d[y],d[z]> ] ] d[x]d[y]d[z]

camps para-eléctrics y para-gravitatoris

camp eléctric:
E_{e}(x,y,z) = kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >


flux[ E_{e}(x,y,z) ] = kq·(1/(ct)^{n})·Q[n]-[ (x_{i})^{-1} ](x,y,z)·xyz
div[ E_{e}(x,y,z) ] = n·kq·( (1/(ct)^{n})·Q[n+(-1)](x,y,z) +...
... (-1)(c/(ct)^{n+1})·Q[n]-[ d_{t}[x_{i}]^{(-1)} ](x,y,z)) )


camp gravitatori:
E_{g}(x,y,z) = (-1)·kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >


flux[ E_{g}(x,y,z) ] = (-1)·kq·(1/(ct))·Q[n]-[ (x_{i})^{-1} ](x,y,z)·xyz
div[ E_{g}(x,y,z) ] = (-1)·n·kq·( (1/(ct)^{n})·Q[n+(-1)](x,y,z) + ...
... (-1)(c/(ct)^{n+1})·Q[n]-[ d_{t}[x_{i}]^{(-1)} ](x,y,z)) )


ecuacions de camp:
flux[ E_{e}(x,y,z) ] = ∭ [ div[ E_{e}(x,y,z) ] ] d[x]d[y]d[z]
flux[ E_{g}(x,y,z) ] = ∭ [ div[ E_{g}(x,y,z) ] ] d[x]d[y]d[z]


ecuacions de camp del temps:
d_{t}[ div[ E_{e}(x,y,z) ] ] = Lap[ E_{e}(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])
d_{t}[ div[ E_{g}(x,y,z) ] ] = Lap[ E_{g}(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])

fisica: electro-magnetisme y gravito-magnetisme

H-E_{e}(r) = k_{e,h}q_{e}·( r^{n}/d_{t}[r]^{n} )
H-E_{g}(r) = (-1)·k_{g,h}q_{g}·( r^{n}/d_{t}[r]^{n} )


H-B_{e}(r) = k_{e,h,m}q_{e}·( d_{tt}^{2}[r]^{n}/d_{t}[r]^{n} )
H-B_{g}(r) = (-1)·k_{g,h,m}q_{g}·( d_{tt}^{2}[r]^{n}/d_{t}[r]^{n} )


ones de so sense massa: m=0
camp emisor:
H-E_{e}(r) + H-B_{e}(r) = 0 <==> ...
... r(t)  = ( sinh( e^{(1/n)·(pi·i)}(kq/kq)t )+ cosh( e^{(1/n)·(pi·i)}(kq/kq)t ) )
camp receptor:
H-E_{e}(r) + H-B_{g}(r) = 0 <==> ...
... r(t)  = ( sinh( e^{(1/n)·(2pi·i)}(kq/kq)t )+ cosh( e^{(1/n)·(2pi·i)}(kq/kq)t ) )
camp receptor:
H-E_{g}(r) + H-B_{e}(r) = 0 <==> ...
... r(t)  = ( sinh( e^{(1/n)·(2pi·i)}(kq/kq)t )+ cosh( e^{(1/n)·(2pi·i)}(kq/kq)t ) )
camp emisor:
H-E_{g}(r) + H-B_{g}(r) = 0 <==> ...
... r(t)  = ( sinh( e^{(1/n)·(pi·i)}(kq/kq)t )+ cosh( e^{(1/n)·(pi·i)}(kq/kq)t ) )

índex de física

índex de etiquetes de física

camps electrics discrets

E(0,0,z)= k_{e}·int-int-int[rho[q]]d[x]d[y]d[ d_{t}[f(t)]z ]·(1/(cm)^{n})·<1,1,1>
on d_{t}[f(t)] es la resistencia del material.


circumferencia
E(0,0,z)= ...
...k_{e}·int-int[0-->2pi][rho[q]]d[sR]d[z]·(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·2pi·R·z
m_{i}d_{tt}[z]=q_{i}·k_{e}(1/(cm)^{n})·rho[q]·2pi·R·z


disc cercle
E(0,0,z)= ...
...k_{e}·int-int[0-->2pi][rho[q]]d[(1/2)·s·R^{2}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·pi·R^{2}( d_{t}[f(t)]z )


esfera plena
E(0,0,z)= ...
...k_{e}·int-int[0-->4pi][rho[q]]d[(1/3)·s·R^{3}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·(4/3)·pi·R^{3}( d_{t}[f(t)]z )


esfera buida
E(0,0,z)= ...
...k_{e}·int-int[0-->4pi][rho[q]]d[s·R^{2}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·4pi·R^{2}( d_{t}[f(t)]z )


doble esfera plena per tall de porta
E(0,0,z)= ...
...k_{e}·int-int[0-->8pi][rho[q]]d[(1/3)·s·R^{3}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·(8/3)pi·R^{3}( d_{t}[f(t)]z )




doble esfera buida per tall de porta
E(0,0,z)= ...
...k_{e}·int-int[0-->8pi][rho[q]]d[R^{2}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·8pi·R^{2}( d_{t}[f(t)]z )


doble esfera:


1 1
2 2


2 2
1 1


doble esfera:


1 2
2 1


2 1
1 2


triple esfera plena per tall de porta
E(0,0,z)= ...
...k_{e}·int-int[0-->12pi][rho[q]]d[(1/3)·s·R^{3}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·4pi·R^{3}( d_{t}[f(t)]z )




triple esfera buida per tall de porta
E(0,0,z)= ...
...k_{e}·int-int[0-->12pi][rho[q]]d[R^{2}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·12pi·R^{2}( d_{t}[f(t)]z )


triple esfera:


1 2
3 1


2 3
1 2


3 1
2 3






quadruble esfera plena per doble tall de porta ortogonal
E(0,0,z)= ...
...k_{e}·int-int[0-->16pi][rho[q]]d[(1/3)·s·R^{3}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·(16/3)pi·R^{3}( d_{t}[f(t)]z )




quadruble esfera buida per doble tall de porta ortogonal
E(0,0,z)= ...
...k_{e}·int-int[0-->16pi][rho[q]]d[R^{2}]d[ d_{t}[f(t)]z ]·...
...(1/(cm)^{n})·<1,1,1>
E(0,0,z)= k_{e}(1/(cm)^{n})·rho[q]·16pi·R^{2}( d_{t}[f(t)]z )


cuadruble esfera:


1 2
3 4


4 3
2 1




2 4
1 3


3 1
4 2


a^{2}=(q_{i}/m_{i})·k_{e}(1/(cm)^{n})rho[q]·V


d_{tt}[ sinh(at^{(-p)}) [o(t)o] (1/(-p))(1/(p+2))t^{p+2} ]=...
...a^{2}( (-p)t^{(-p)+(-1)}sinh(at^{(-p)}) )


d_{tt}[ sinh( a·(bt^{2}+ct) ) [o(t)o] (1/(2b))·ln(2bt+c) ]=...
...a^{2}(2bt+c)sinh( a·(bt^{2}+ct) )

ones electro-magnétiques y gravito-magnétiques

E_{e}(r) = k_{e}q_{e}·( 1/r^{n} )
E_{g}(r) = (-1)·k_{g}q_{g}·( 1/r^{n} )


B_{e}(r) = (-1)·k_{e,m}q_{e}·( d_{t}[r]^{n}/r^{n} )
B_{g}(r) = k_{g,m}q_{g}·( d_{t}[r]^{n}/r^{n} )


divergencia y laplacià del camp eléctric y gravitatori:
d_{r}[ E_{e}(r) ] = (-n)·kq·(1/r^{n+1})
d_{rr}^{2}[ E_{e}(r) ] = (-n)((-n)+(-1))·kq·(1/r^{n+2})


d_{r}[ E_{g}(r) ] = (-1)·(-n)·kq·(1/r^{n+1})
d_{rr}^{2}[ E_{g}(r) ] = (-1)·(-n)((-n)+(-1))·kq·(1/r^{n+2})


divergencia y laplacià del camp magnétic:
d_{r}[ B_{e}(r) ] = (-1)·(-n)·kq·( d_{t}[r]^{n}/r^{n+1} )
d_{rr}^{2}[ B_{e}(r) ] = (-1)·(-n)((-n)+(-1))·kq·( d_{t}[r]^{n}/r^{n+2} )


d_{r}[ B_{g}(r) ] = (-n)·kq·( d_{t}[r]^{n}/r^{n+1} )
d_{rr}^{2}[ B_{g}(r) ] = (-n)((-n)+(-1))·kq·( d_{t}[r]^{n}/r^{n+2} )


ecuacions de camp del temps:
d_{t}[ d_{r}[ E_{e}(r) ] ] = d_{rr}^{2}[ E_{e}(r) ]·d_{t}[r]
d_{t}[ d_{r}[ B_{e}(r) ] ] = d_{rr}^{2}[ B_{e}(r) ]·d_{t}[r]


d_{t}[ d_{r}[ E_{g}(r) ] ] = d_{rr}^{2}[ E_{g}(r) ]·d_{t}[r]
d_{t}[ d_{r}[ B_{g}(r) ] ] = d_{rr}^{2}[ B_{g}(r) ]·d_{t}[r]


d_{t}[ d_{r}[ E_{e}(r)+B_{e}(r) ] ] = d_{rr}^{2}[ E_{e}(r)+B_{e}(r) ]·d_{t}[r]
d_{t}[ d_{r}[ E_{g}(r)+B_{g}(r) ] ] = d_{rr}^{2}[ E_{g}(r)+B_{g}(r) ]·d_{t}[r]


d_{tt}^{2}[r] = 0 <==> r(t)  = (k_{e}/k_{e,m})^{(1/n)}·t
d_{tt}^{2}[r] = 0 <==> r(t)  = (k_{g}/k_{g,m})^{(1/n)}·t


d_{t}[ d_{t}[ E_{e}(r)+B_{e}(r) ]·( 1/d_{t}[r] ) ] = d_{rr}^{2}[ E_{e}(r)+B_{e}(r) ]·d_{t}[r]


d_{tt}^{2}[ E_{e}(r)+B_{e}(r) ]·( 1/d_{t}[r] ) +...
... (-1)·d_{r}[ E_{e}(r)+B_{e}(r) ]·( d_{tt}^{2}[r]/d_{t}[r] ) =...
... d_{rr}^{2}[ E_{e}(r)+B_{e}(r) ]·d_{t}[r]


ecuacions de front de ones:
d_{tt}^{2}[ E_{e}(r)+B_{e}(r) ] = d_{rr}^{2}[ E_{e}(r)+B_{e}(r) ]·d_{t}[r]^{2}
d_{tt}^{2}[ E_{g}(r)+B_{g}(r) ] = d_{rr}^{2}[ E_{g}(r)+B_{g}(r) ]·d_{t}[r]^{2}