# Notes on "Equipotential Curves"

The point of this experiment is to show you the relationship between voltage and the electric field. You will make measurements of the voltage at a number of points in a pan of water, and then use those measurements to calculate the electric field between the points.

There is a useful analogy which may help you to understand the connection between voltage and electric field.

```
On a topographic map           In your experiment today
----------------------------------------------------------------
(x, y) position is shown     |      (x, y) position is shown
|
|
contour lines indicate       |        contour lines indicate
ALTITUDE                |               VOLTAGE
|
|
calculate the SLOPE of ground  |  calculate the ELECTRIC FIELD
like so:               |             like so:
|
change in altitude   |             change in voltage
slope =  -----------------    |  E field =  -----------------
change in position   |             change in position
|
|
(meters)         |               (volts)
=  -----------------    |          =  -----------------
(meters)         |               (meters)
|
```

On a topographic map, slope is the derivative of altitude, with respect to position. On the map of your experiment, the electric field is the derivative of voltage with respect to position.

• Does altitude have a direction?
• Does slope (of the ground) have a direction?

• Does voltage have a direction?
• Does electric field have a direction?

Here's an example of a topographic map: a section of the 7.5-minute series around Phoenicia, New York. The contour lines are at 20-foot intervals. Click on the map to see the full-size version.