About the midterm exam
It will be an oral exam. Schedule a half-hour appointment with Paul once you have solved the problem(s) below and studied to your satisfaction.
Bring
You will be given a photocopy, or access to the material inside the front and back covers of Griffiths. (E.g. curls and gradients in different coordinate systems, physical constants, etc.)
Chapter 1
- Differentiation, $\myv \grad$, $\myv \grad\cdot$, $\myv \grad\times$.
- Line, surface, volume integrals.
- Fundamental theorem for gradients (Relation of $\myv E$ to $V$).
- Fundamental theorem for divergence (basis of Gauss' law).
- Cartesian and non-Cartesian coordinate systems.
- Dirac delta functions.
Chapter 2 - Electrostatics
- Coulomb's law, the electric field, principle of superposition.
- Integrating over a continuous charge distribution to get $\myv E$.
- Electric field lines (qualitative), conventions for drawing
- Divergence of the electric field $\myv \grad\cdot E=\frac{1}{\epsilon_0}\rho$. Gauss' law: meaning and application. Fields in high-symmetry situations (planes, spheres, cylinders).
- $\myv \grad \times \myv E=0$ (curlless field) implies that there's a potential $V$ such that $\myv E=-\myv \grad V$. Integrating $\myv E$ to get potential differences.
- Griffith's figure 2.35 is a summary of relations between $\myv E$, $V$, and $\rho$.
- Work / energy of charge distributions
- Conductors
- Capacitance