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Monday, October 13, 2014

Scent Of Beauty...

This is obviously a joke.

From the previously post "Magnetic Field In General, HuYaa",

Bt=iEx

Bxxt=iEx

Since,  i.i=1,

Bxxt=i1(i.i)Ettx

Bxxt=Et1itx

and  i rotates  x  to  r,  the radial distance,

Bxxt=Ettr=Etxrtx

Bx(xt)2=Etxr

Integrating by x  and by  r,

Bx(xt)2dxdr=Etxrdxdr

Since, for an electromagnetic wave,

(xt)2=c2=(1εoμo)2=1εoμo

dBdr=εoμoEtdxdx

Bdr=εoμot{E(dx)2}

If  Bdr  is around a square loop with length  dx and height also  dx,  bear in mind that r is perpendicular to  x,  then,

Bdr=εoμot{EdA}

Which is Maxwell's  displacement current.  This is the last of Maxwell's Equations not considering current density,  je.

The maths is not rigorous but it seems to indicate that dynamically all that is needed is,

Bt=iEx

to define the  B  field established by moving charges.  I have to think about this one.