\(\oint _{ 2\pi a_{ \psi } }{ E_{ \psi } } \, d\, \lambda =-\cfrac { 1 }{ c^{ 2 } } \cfrac { d }{ d\, t } \left\{ \oint _{ \pi a^{ 2 }_{ \psi } }{ F_{ \psi } } dA_{ l } \right\}\)
and
\(\varepsilon _{ o }\oint _{ 2\pi a_{ \psi } }{ E_{ \psi } } d\, \lambda =\oint _{ \pi a^{ 2 }_{ \psi } }{ \rho } \, d\, A_{ l }\)
We have,
\(\varepsilon _{ o }\oint _{ 2\pi a_{ \psi } }{ E_{ \psi } } d\, \lambda =\oint _{ \pi a^{ 2 }_{ \psi } }{ \rho } \, d\, A_{ l }=-\cfrac { 1 }{\mu_o } \cfrac { d }{ d\, t } \left\{ \oint _{ \pi a^{ 2 }_{ \psi } }{ F_{ \psi } } dA_{ l } \right\}\)
An \(E_\psi\) in a circle confines a sheet of particles of density \(\rho\) in the area of the circle, through which we have a time varying flux, \(\Psi\),
\(\cfrac { \partial\,\Psi }{ \partial\, t }=\cfrac { \partial }{ \partial\, t } \left\{ \oint _{ \pi a^{ 2 }_{ \psi } }{ F_{ \psi } } dA_{ l } \right\}\)
In the last expression, either \(F_\psi\) is time varying or the area \(A_l\) is made to vary in time. In the latter case,
\(\cfrac { \partial\,A_l }{ \partial\, t }=2\pi a_\psi\cfrac { \partial\,a_\psi }{ \partial\, t }\)
In which case, we can have a thin surface like a drum surface vibrating in and out of the confine of the circle. The points over the surface are not in phase. The normal at each surface point is swinging such that \(\hat{F_\psi}\cdot n_{A_l}=cos\left(\theta(t)\right)\) is time varying.
Such time varying effects will be seen as ripples across the surface. \(F_\psi\) can be kept constant.
Just like Stargate.
