Section 20.6 Electric Field Vector Maps
Electric fields exist in three dimensions of space around any charge or charge distribution. One of the major conceptual difficulties when first encountering the idea of electric fields, is that interacting with the field through our primary senses of sight, sound and touch is not possible. Electric and gravitational fields are invisible, and we can really only measure their effect on other objects through the forces they exert or through indirect measurement of the potential difference, a subject for a later chapter.
Electric field vector maps offer us a way to visualize what the field might look like in space:
Representation 20.6.1. Electric Field Vector Map.
An electric field vector map shows a vector at many different points in space to highlight the direction and magnitude of the electric field in different regions of space. The electric fields can be different at every point in space, so you should always draw enough vectors to get a good sense for how the field is changing.
For a given point in space, electric field vector maps tell us how big and in what direction the electric field is.
Exercises Activities
1. Practice Sketching Field Maps.
Sketch (by hand) a vector map for the following field in the \(xy\)-plane: \(\vec{S} = x \hat{x} + y \hat{y}\text{.}\) Sketch at least 20 vectors showing how this vector field changes in both directions.
2. Practice Sketching Field Maps.
Use a graphing calculator (such as
Desmos) to sketch the following electric field in the
\(xy\)-plane:
\(\vec{E} = \frac{7x}{\sqrt{x^2+y^2}} \hat{x} + \frac{7y}{\sqrt{x^2+y^2}} \hat{y}\text{.}\)
