## Illustration 23.1: What is an Electric Field?

Please wait for the animation to completely load.

This animation plots a vector field when you enter values for the x component and y component of the field. You should try several values to get a sense of what a vector field is. Restart.

Begin by creating a simple uniform vector field by entering 5 N/C for E_{x} and updating the field. Notice that the animation displays a grid of arrows pointing to the right. If you enter -5 N/C for E_{x}, the field arrows will point in the opposite direction. Enter 3 N/C for E_{x} and 4 N/C for E_{y} and update the field again. The arrows now point at an angle of 37 degrees with respect to the x axis. Now, if you enter 2 N/C for E_{x}, what do you see? How is it different from 5 N/C for E_{x}? What does the color of the vector show? Why do you think we do not represent magnitude of the vector field by the length of the vector?

Now, build a field that you are familiar with (whether you know it or not) by putting in 0 N/C for E_{x} and -4.9 N/C for E_{y}. This is a representation of the vector force field for a 0.5-kg mass close to Earth's surface. Why? What would the vector force field be for a 3-kg mass close to Earth's surface? (If it is far away from Earth's surface, like a satellite in orbit, you need to take into account the decrease in gravitational attraction as a function of distance squared).

The values of the field components do not need to be constants. Try 2*x for E_{x} and 2*y for E_{y}. What do you see? In this case, the vectors show you a field that changes in both magnitude and direction with position. For x = 0 m, y = 2 m, what are the values of E_{x} and E_{y}? Does the arrow on the screen point in the correct direction at that point? Repeat this exercise with 2*y for E_{x} and 2*x for E_{y}.

Try some other set of (nonconstant) values for E_{x} and E_{y}. Specifically, try E_{x} = x/(x*x + y*y)^3/2 and E_{y} = y/(x*x + y*y)^3/2. What does this vector field look like?

Illustration authored by Anne J. Cox.

Script authored by Mario Belloni and Wolfgang Christian.