## 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.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

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