Charge

There are two directions at work in Coulomb forces. One is the sign that results from Coulomb's Law—whether the force is attractive or repulsive. But the other is what direction "attraction" or "repulsion" actually acts in, which is completely dependent on the geometry of the charge configuration. Attraction and repulsion will both always act along the line between the two charges, with attraction pulling them together and repulsion pushing them apart.

Electric Fields

The hardest part of a problem using Gauss' Law is usually figuring out exactly what kind of Gaussian surface to draw. Nine times out of ten, it's either going to be a sphere (point charges, charged spheres, etc.) or a cylinder (charged rods, charged sheets, conductors, etc.).

Electric Potential

The formulas for F_e, E, V, and U_e all look very similar—an easy way to make sure you're using the right one is to check the units. Forces (F_e) are in N, electric fields (E) are in N/C, electric potentials (V) are in V or J/C, and electric potential energies are in J.

Basic Circuit Elements

Did we mention Ohm's Law? It's V = IR. This applies to only one circuit element at a time—one resistor, for example—but in the next section we see how to mathematically combine multiple elements together in order to use Ohm's Law on more complex circuits.

Solving Circuit Questions

Kirchhoff's Current Law applies to nodes; Kirchhoff's Voltage Law to loops. Remember what each says (current in equals current out / voltage applied equals voltage lost) and you'll cruise through complicated circuits no problem.

Magnetic Fields

The key insight in Ampère's Law is that the product Bl only corresponds to the component of B that is parallel to l. If your Ampèrian loop is a square drawn in a horizontal magnetic field, only two sides of the square will contribute to l—the two vertical sides have no effect.

Magnetic Forces

The right hand rule can be... unruly. Remember Index finger is for current (I for an I), Middle finger is for Magnetic field, and your thumb is the result.

Electromagnetic Induction

Lenz's Law is straightforward to understand, but can be tricky to apply. Make sure your right hand rule is right.

Advanced Circuit Elements

Resistors and inductors combine identically, but don't forget that capacitors are backwards—they combine in series like resistors combine in parallel, and vice versa.