equals $(l-1)/2$.

An important parameter is the $Q$ factor $$\label{3-16} Q_{\text{rad}}=\frac{\omega'}{2\omega''}=
2\,\pi\,\frac{\text{stored energy}}{\text{radiated energy per
cycle}}\,{.}$$ For exterior modes the value of $Q_{\text{rad}}$ is always less than 1, hence these modes can never be observed as sharp resonances. At the same time for $\varepsilon $ greater than 5, the $Q_{\text{rad}}$ for interior modes is greater than 10 and it can reach very high values when $\varepsilon \to \infty$.

For physical implications more important is the classification in terms of [*volume*]{} or [*surface*]{} modes according to whether $r> l$ or $l> r$. For volume modes the electromagnetic energy is distributed in the whole volume of the sphere while in the case of surface modes the energy is concentrated in the proximity of the sphere surface. The exterior modes are the first roots of the characteristic equations and it can be shown that they are always surface modes.

![Electric energy density $r^2\,E_{\text{t}}^2$ for the surface (A) and volume (B) TE-modes of a dielectric sphere with $\varepsilon =40$ placed in vacuum.[]{data-label="Plot:s-v-modes"}](pic1.eps "fig:"){width="75mm"} ![Electric energy density $r^2\,E_{\text{t}}^2$ for the surface (A) and volume (B) TE-modes of a dielectric sphere with $\varepsilon =40$ placed in vacuum.[]{data-label="Plot:s-v-modes"}](pic2.eps "fig:"){width="75mm"}

Figure 1 shows a typical spatial behaviour of 