From the post "So, So What?",
∂2Uloss∂θ2=cos(2θ)[μoB2{1−(μoμa)2}−εoE2{1−(εaεo)2}]
then we come to the term,
[μoB2{1−(μoμa)2}−εoE2{1−(εaεo)2}]
which we observe, flips the sign of the expression with increasing E. An increase in E can switch the system from minimum loss to maximum loss.
So, a pointy antenna has low loss only if E is keep within a range,
E2<B2μoεo{1−(μoμa)2}{1−(εaεo)2}
And as long as E is kept high, a flat antenna has minimum loss,
B2<E2εoμo{1−(εaεo)2}{1−(μoμa)2}
So, So, So, What?