2017-14.md

course	course_year	question_number	tags	title	year
Electromagnetism	IB	14	IB 2017 Electromagnetism	Paper 2, Section I, $\mathbf{6 C}$	2017

State Gauss's Law in the context of electrostatics.

A spherically symmetric capacitor consists of two conductors in the form of concentric spherical shells of radii $a$ and $b$, with $b>a$. The inner sphere carries a charge $Q$ and the outer sphere carries a charge $-Q$. Determine the electric field $\mathbf{E}$ and the electrostatic potential $\phi$ in the regions $r<a, a<r<b$ and $r>b$. Show that the capacitance is

$$C=\frac{4 \pi \epsilon_{0} a b}{b-a}$$

and calculate the electrostatic energy of the system in terms of $Q$ and $C$.