Section 21.6 Electric Field Vector Maps
Subsubsection Key Ideas
Electric fields exist in three dimensions of space around any charge or charge distribution. Electric field vector maps offer a way to visualize the field’s key properties:
Representation 21.6.2. Electric Field Vector Map.
An electric field vector map uses a vector at different points in space to highlight the direction and magnitude of the electric field. The electric field can have a different value at every point in space, so you should draw enough vectors to portray any key features in how the field changes.
Subsubsection Activities
Activity 21.6.1. 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.
Activity 21.6.2. Practice Sketching Field Maps.
Use a graphing calculator (such as
Desmos) to sketch the following electric field in the \(xy\)-plane: \(\vec{E} = \frac{7x}{\sqrt{x^2+y^2}} \hat{x} + \frac{7y}{\sqrt{x^2+y^2}} \hat{y}\text{.}\)
