Electrostatic Devices

The Capacitor

Problem #$1$

A spherical capacitor is located at the origin of a cartesian coordinate system. It consists of two concentric spherical conductors with homogeneous dielectric material $lon$ in between the conductors, as shown in the figure below, left.

The inner conductor has radius $a,$ and the outer conductor has radius $b,$ as shown in the figure below, right. Equal charges $+Q$ and $-Q$ are placed on the inner and outer conductors, respectively.

$($a$)$ Following the steps outlined in the course notes, determine the capacitance of the spherical capacitor. Number the steps and show all work.

$($b$)$ With the expression you found in part $($a$),$ find the capacitance of the spherical shell if the inner radius is $a=2cm,b=2\mathrm{.}5cm,$ and the dielectric medium has relative permittivity $lo{n}_r=12\mathrm{.}25$