So, So, So, What! Oops.

From the post "So, So, So, What?"  A flat antenna has low loss,

$U_{loss}=\cfrac{1}{2}\left[\varepsilon_oE^{ 2 }cos^{ 2 }(\theta )\left\{ 1-(\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } )^{ 2 } \right\}+\mu_oB^{ 2 }sin^{ 2 }(\theta )\left\{ 1-(\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 } \right\}  \right]$

$\cfrac { \partial \, U_{ loss } }{ \partial \, \theta  } =\cfrac{1}{2}sin(2\theta )\left[ \mu _{ o }B^{ 2 }\left\{ 1-(\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 } \right\} -\varepsilon _{ o }E^{ 2 }\left\{ 1-(\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } )^{ 2 } \right\}  \right]$

$\cfrac { \partial ^{ 2 }\, U_{ loss } }{ \partial \, \theta ^{ 2 } } =cos(2\theta )\left[ \mu _{ o }B^{ 2 }\left\{ 1-(\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 } \right\} -\varepsilon _{ o }E^{ 2 }\left\{ 1-(\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } )^{ 2 } \right\}  \right]$

when  $\theta=90^o$, $\cfrac { \partial \, U_{ loss } }{ \partial \, \theta  } =0$  and $cos(2\theta)=-1$.  The term from the second derivative,

$\mu _{ o }B^{ 2 }\left\{ 1-(\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 } \right\} -\varepsilon _{ o }E^{ 2 }\left\{ 1-(\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } )^{ 2 } \right\}$

can determines whether it is maximum or minimum loss.

For copper,

$\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } \rightarrow\infty$

$\cfrac { \mu _{ o } }{ \mu _{ a } }$=1/0.999994= 1.000006

This term simplifies to

$\varepsilon _{ o }E^{ 2 }\left\{ (\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } )^{ 2 }-1 \right\} -\mu _{ o }B^{ 2 }\left\{ (\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 }-1 \right\}$

for minimum loss,

$\mu _{ o }B^{ 2 }\left\{ (\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 }-1 \right\} \gt\varepsilon _{ o }E^{ 2 }\left\{ (\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } )^{ 2 }-1 \right\}$

$B^{ 2 }\gt\cfrac { \varepsilon _{ o } }{ \mu _{ o } } E^{ 2 }\frac { \left\{ (\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } )^{ 2 }-1 \right\}  }{ \left\{ (\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 }-1 \right\}  }$

such that over all,

$\cfrac { \partial ^{ 2 }\, U_{ loss } }{ \partial \, \theta ^{ 2 } }\gt0$

In general,

$\cfrac { \varepsilon _{ o } }{ \mu _{ o } } = (c\varepsilon _{ o } )^2$= (299792458*8.8541878176e-12)^2 = 7.046e-6

which makes the inequality possible even without  $B$  very large.  Any material with a relative permittivity greater than one, but a relative permeability less than one (diamagnetic), graphite and sealed mercury, are suitable as flat antenna material.  (Sliver is not suitable because of its high permittivity which would require a high $B$.)

A coil is a flat antenna.  And from the post "The Third Wave",

$\nabla \times Y=-\cfrac { 4\pi  }{ c^{ 2 } } \cfrac { \partial \, j_{ e } }{ \partial t }$

$j_e$  set off  a wave perpendicular to the direction of  $Y$.

And the loss of this type of antenna,

$U_{loss}=\mu_oB^{ 2 }sin^{ 2 }(\theta )\left\{ 1-(\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 } \right\}$

since,

$1-(\cfrac { \mu _{ o } }{ \mu _{ a } } )^{ 2 } \lt0$

we have a small gain.

Why forgone the gain from the term

$1-(\cfrac { \varepsilon _{ a } }{ \varepsilon _{ o } } )^{ 2 }$?

Because a high  $E$  will give you cancer.  In practice, whether such an antenna will be effective is speculative.  Try else never know.