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Study Guide

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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.

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.).

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.

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.

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.

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.

The right hand rule can be... unruly. Remember *I*ndex finger is for current (I for an *I*), *M*iddle finger is for *M*agnetic field, and your thumb is the result.

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

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.

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