Examen de electro-magnetismo:
Principio:
E(x,y,z) = qk·(1/r)^{3}·a·< x^{2},y^{2},z^{2} >
E(yz,zx,xy) = qk·(1/r)^{4}·a^{2}·< (yz)^{2},(zx)^{2},(xy)^{2} >
Ley:
div[ E(x,y,z) ] = ?
Anti-div[ E(yz,zx,xy) ] = ?
Ley:
Anti-Potencial[ E(x,y,z) ] = ?
Potencial[ E(yz,zx,xy) ] = ?
Ley: [ de corrección del examen ]
div[ E(x,y,z) ] = d_{x(yz)}^{2}[ Anti-Potencial[ E(x,y,z) ] ]
Anti-div[ E(yz,zx,xy) ] = d_{x(yz)}^{2}[ Potencial[ E(yz,zx,xy) ] ]
Ley:
Sea ( d_{t}[ I_{cx} ] = 0 & d_{t}[ I_{cy} ] = 0 ) ==>
Si d[M_{1}(t)] = (1/2)·mgx·(1/s)^{2}·cos(nw)·d[w] ==>
M_{1}(t) = (1/2)·mg·(x/n)·(1/s)^{2}·sin(nw)
Si d[ d[M_{2}(t)] ] = mg·(1/s)^{2}·sin(nw)·cos(nw)·d[y]d[w] ==>
M_{2}(t) = mg·(y/n)·(1/s)^{2}·(1/2)·( sin(nw) )^{2}
M_{1}(t) = M_{2}(t) <==> ( w(t) = (1/n)·arc-sin( I_{cx}/I_{cy} ) & I_{cx} [< I_{cy} )
Ley:
Sea d_{t}[ I_{c} ] = 0 ==>
Si d[M_{1}(t)] = (1/2)·I_{c}·u^{2}·cos(nw)·d[w] ==>
M_{1}(t) = (1/2)·I_{c}·u^{2}·(1/n)·sin(nw)
Si d[ d[M_{2}(t)] ] = I_{c}·u^{2}·(1/x)·sin(nw)·cos(nw)·d[x]d[w] ==>
M_{2}(t) = I_{c}·u^{2}·ln(ax)·(1/n)·(1/2)·( sin(nw) )^{2}
M_{1}(t) = M_{2}(t) <==> ( w(t) = (1/n)·arc-sin( ( 1/ln( aI_{c}·(1/(md)) ) ) ) & aI_{c} >] md·e )
