Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.
Lecture 1 | Field Model, Charges in an Electric Field
Electric Fields
Lecture 1 | Field Model, Charges in an Electric Field
Electric Fields
Spiders ride electric fields to fly hundreds of miles.
Pre-lecture Study Resources
Electric Fields | Field Model and Charges in an Electric Field
Field Theory
A field is a map. It tells you how navigating a region of space may go before you even get there. Imagine a room being warmed by a fireplace in the corner. I could walk to every point in the room, staring with position $\overrightarrow{r}=<0,0,0> m$, and record the temperature in a data table. That table represents the temperature field of the room. That scalar field could then be used to deduce heat transfers in the room. Fields are maps, where every point in space there is information (usually a scalar or a vector), that can be used to explain interactions. Fields are constructs, more than any other we've encountered. They are not observable in any conventional way but are rather a conceptual tool for the study of interactions.
An example of a vector field is a velocity field. Instead of every point in space containing one number, like in the temperature field example, every point in space contains three numbers which are the x, y, and z components of the velocity. A stream that narrows could possibly be described by the velocity field below.
Vector field of a moving river
Even though there are not vectors drawn everywhere in the stream does not mean the field is zero at those points, its merely due to the limitation of how many vectors are feasible (and useful) to draw. Now a rubber ducky floating down the river could have a somewhat predictable interaction with the river. It would speed up in the narrow region and possibly change directions if it entered from the bottom. Be careful, the temperature and velocity field examples are not the same as the electric field and potential. They are only used to get a loose feel for the concept.
The Electric Field
All charges create electric fields. We say the charge alters the space around it but this not true in any real way, that is what mass does. Charges rather create a field that can travel through the vacuum of space and influence other charges to feel a force. Consider the situation below where $Q$ is a positive charge that generates the vector field shown. That is the field owned by charge $Q$.
Point charge electric field
A second charge $q_0$, whose field is not being shown, resides in $Q's$ field. We call $q_0$ the test charge since we are not considering the field it creates. If the electric field from $Q$ is considered to be $\overrightarrow{E}$, then the force that field puts on the test charge follows the following equation.
Force on a Test Charge ($q_0$) in an Electric Field ($\overrightarrow{E}$)
$\overrightarrow{F_0}=q_0 \overrightarrow{E}$
The essence of an electric field lies in this example. The charge $Q$ generates a field that a second charge $q_0$ feels a force from and in that way they interact. This model gives $Q$ ownership to something that can exist without the presence of the second charge. After all, there would be no such thing as a Coulomb force if the second charge didn't exist. It is this reason some consider the electric field to be more fundamental and elegant than Coulombs Law.
Key Equations and Infographics
Net Charge of a System
Electric Force
Force on a Test Charge in an Electric Field
A representation with the words electron slash proton charge on the top. There is an equation that shows that the elementary charge of a proton is equal to positive one point six, zero, two by ten to the nineteenth power. The elementary charge of an electron is equal to negative one point six, zero, two by ten to the nineteenth power. This is also written in words below.
Now, take a look at the pre-lecture reading and videos below.
Required Videos
OpenStax Section 18.4 | Electric Field: Concept of a Field Revisted
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