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) )