FIGURE 6.41 For Problem 6.46.
FIGURE 6.42 For Problem 6.48.
6.45 A spherical capacitor has inner radius $d$ and outer radius $a$. Concentric with the spherical
conductors and lying between them is a spherical shell of outer radius $c$ and inner radius
$b$. If the regions $d < r < c$, $c < r < b$, and $b < r < a$ are filled with materials with per-
mittivites $\epsilon_1$, $\epsilon_2$, and $\epsilon_3$, respectively, determine the capacitance of the system.
6.46 Determine the capacitance of a conducting sphere surrounded by a thick spherical shell
as shown in Figure 6.41.
6.47 A coaxial cable has inner radius of 5 mm and outer radius of 8 mm. If the cable is 3 km
long, calculate its capacitance. Assume $\epsilon = 2.5\epsilon_o$
6.48 A capacitor consists of two plates with equal width ($b - a$), and a length $L$ in the
$z$-direction. The plates are separated by $\phi = \pi/4$, as shown in Figure 6.42. Assume that
the plates are separated by a dielectric material ($\epsilon = \epsilon_{\epsilon_r}$), and ignore fringing. Determine
the capacitance.
6.49 Calculate the capacitance of a coaxial cable with inner
