Capturing a \(T^{+}\) particle in a \(B\) orbit due to a spinning electron.
We are getting warmer!
Consider a charge on approach to a disc of radius \(r\),
The total perpendicular \(E\) field component through the area of the disc is,
\(E_A=\int_{0}^{r} {2\pi xtan(\theta). Ecos(\theta) }d\,r\)
where the electric field from the charge is
\(E=E_oe^{-\cfrac{x}{a_{e}}}\)
the exponential form of an electric field analogous to the exponential form of the expression for gravity field.
\(E_A=\int_{0}^{r} {2\pi xtan(\theta). E_oe^{-\cfrac{x}{a_{e}cos(\theta)} }cos(\theta) }d\,r\)
the distance of the elemental ring from the charge is \(\cfrac{x}{cos(\theta)}\)
\(E_{ A }=2\pi E_{ o }\int _{ 0 }^{ r }{ xtan(\theta )e^{-\cfrac{x}{a_{e}cos(\theta)} }cos(\theta) } d\, r\)
and the change of \(E_A\) with time \(t\),
\(\cfrac { \partial \, E_{ A } }{ \partial t } =2\pi E_{ o }\cfrac { \partial \, }{ \partial t }\int _{ 0 }^{ r }{ xtan(\theta )e^{-\cfrac{x}{a_{e}cos(\theta)} } cos(\theta)} d\, r\)
this was in the post "Electron Orbit B Field II" dated 17 Oct 2014, corrected for the term \(cos(\theta)\) to consider normal component of \(E\) through the disc.
The reason why the normal component through the disc was not taken is because later the electron travels in a circle away from the axis through the center of the disc. If the normal component is taken again by multiplying \(cos(\phi)\), some \(E\) field lines will be lost. As those taken out previously by multiplying \(cos(\theta)\), are now rotated and are normal to the disc.
I must be tired!
So, we are back to, the time varying \(E\) field through a disc is
The reason why the normal component through the disc was not taken is because later the electron travels in a circle away from the axis through the center of the disc. If the normal component is taken again by multiplying \(cos(\phi)\), some \(E\) field lines will be lost. As those taken out previously by multiplying \(cos(\theta)\), are now rotated and are normal to the disc.
I must be tired!
So, we are back to, the time varying \(E\) field through a disc is
\(\cfrac { \partial \, E_{ A } }{ \partial t } =2\pi E_{ o }\cfrac { \partial \, }{ \partial t }\int _{ 0 }^{ r }{ xtan(\theta )e^{-\cfrac{x}{a_{e}cos(\theta)} } } d\, r\)
And the diagram that causes strabismus is back.
Have a nice day.
