# A Useful Metaphor

It can be useful, when thinking about electric potential in space, to compare it to the height (or elevation) of a landscape:
• Every point on a landscape has a particular height h, just as every point in space has an electric potential V.
• If we place an object with weight mg at a point with height h, it has a gravitational potential energy $$mg\times h$$. Similarly, if we place a charge $$q_t$$ at a location with potential V, it has an electric potential energy $$q_tV$$.
• For most practical purposes, only changes in elevation matter: you're much more likely to notice how flat Kansas is, than that it is over half a kilometer above sea level. Similarly, only changes in electric potential matter.

In terms of this metaphor, positive target charges like to move "downhill", because they tend to move towards lower potential. (Positive charges are like boulders that way.) Negative target charges, however, like to move towards higher potential, and so they tend to move "uphill". (Helium balloons?)

If target charges move around the potential landscape, source charges create the potential landscape. As shown in the first graph, positive source charges create peaks or hills in the landscape (or more technically, "local maxima in the potential function"). A positive target placed near this peak will move downhill, as if it were repelled by the top of the hill. Negative charges, by rolling uphill, will be attracted to the positive source charge. The second graph shows a negative source charge forming a crater or dip in the potential landscape, which attracts positive charges and repels negative ones.

What direction will the positive charge move, in this picture?
A) to the left B) to the right

Positive charges like to move downhill towards lower potential. Thus the positive charge will move to the left.
A source charge creates the electric potentials shown. The source charge is
A) positive B) negative

The potential gets larger as we move closer to the source charge. Thus when we move closer to the charge we move uphill, and so the source charge is positive.

[TO BE CREATED SOMEDAY] Click the x axis to add a positive or negative source charge, and watch the potential landscape change. Click on the landscape to add a target charge and see how it reacts.
[TO BE CREATED SOMEDAY] Quiz that alternates between source and target. Source: show a few potential values, what source is creating it? Target: show some potential values, what direction would the charge move?