Section 9.4 Electric Field Vector Maps
To visualize what an electric field might look like in space, we can use electric field vector maps:
Representation 9.4.1. 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:
\(\vec{E} = \frac{7x}{\sqrt{x^2+y^2}} \hat{x} + \frac{7y}{\sqrt{x^2+y^2}} \hat{y}\text{.}\)
