The electric field from a distribution of charge, like that on a charged rod, is fundamentally a superposition of all the fields from the individual charges. Electric fields add by the principle of superposition, which is to say they add linearly and like all other vectors we've learned about.

$\overrightarrow{E}_{net} = \sum \overrightarrow{E}_i$

Sometimes the physics representation of a field is presented in the form of Field Lines, where the strength of the field is larger where the lines are more closely spaced. In the field line representation, field lines start at positive charges and end on negative charges. The diagram above is the electric field for a dipole.

Through superposition, the net field for a number of charge distributions can be determined. It's interesting to note that the electric field for a zero dimensional charge (a point charge) falls off like 1/r² - the field for a one dimensional line of charge falls off like 1/r - and the field from a two dimensional sheet of charge doesn't fall off at all. It's no coincidence that as you increase the dimensions of the charge distribution, the field decreases how fast it falls off.

The Electric Field due to an Infinite Sheet of Total Charge $Q$

$|\overrightarrow{E}_{net}| = \frac{Q}{2 \epsilon_0 A}$, where $\epsilon_{0} = 8.85 x 10^{-12} F \cdot m^{-1}$, and $A$ is the area of the sheet.

If the sheet is infinite or you are close to a finite sheet, the field doesn't even decrease with increased distance. As you move further away from the plate, the electric fields from charges further and further away start to add more constructively, causing the field to remain constant. Putting two plates separated by some distance, with opposite charges, is called a Parallel Plate Capacitor. The fields inside the plates are uniform and provide an excellent tool for studying electric fields.

Now, take a look at the pre-lecture reading and videos below.

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