Solution
= Solution
For $f(x)=V_0x/L$, direct integration gives
$$
ΔE_{\rm Rad}={q^2μ_0\over3πm^2c}\sqrt{m/2}{V_0\over L}
(\sqrt E-\sqrt{E-V_0}),\qquad E>V_0,
$$
and
$$
ΔE_{\rm Rad}={2q^2μ_0\over3πm^2c}\sqrt{m/2}{V_0\over L}\sqrt E,
\qquad E<V_0.
$$
The reflected expression increases up to threshold and the transmitted expression decreases above it. The supremum is therefore approached from below at $E=V_0$ and equals
$$
\boxed{{2q^2μ_0\over3πm^2c}\sqrt{m/2}{V_0^{3/2}\over L}.}
$$