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# Equipotential Lines

### What do we know about analogies? If we say that A is like B, then logically A is not B! They have some behaviors in common, but in others ways they must be different. (Otherwise A and B would not be analogous, but rather identical.)

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# What is a topographic map?

### How do we make a topographic map?

Compare overhead view with the side profile view.

### Here are some topographic map examples.

Topographic maps 3D computer model: Class Zone

Topographic maps 3D – Second example: Class Zone

Mount Washington 3D Topographical Map Animation

White Mountain National Forest 3D Topographical Map Flythrough Animation

New Hampshire White Mountains Rivers 3D Map Animation

## What does this have to with potential energy?

Caution: in the top panel, h is HEIGHT.  In the bottom panel, we’re not talking about physical height, but a difference in the strength of the electric field.

### Electric Potential: Visualizing Voltage by Eugene Khutoryansky

Analogy completed:

Voltage is electrical potential energy/unit charge

Map contour lines show us lines of equal elevation ( = GPE/unit mass , overhead view)

Equipotential lines show us equal electric potential lines (lines of equal voltage)

Every point on a contour line is at the same elevation.

Every point on an equipotential line is at the same voltage (electric potential.)

Such maps can be thought as topographic maps. Consider the map of Nashoba Hill:

from Google Maps, using the elevation option

Water always flows downhill, hence rivers are always perpendicular to lines on the topographic map

Similarly, electric field lines are always perpendicular to equipotential lines.

When map lines are close together, the slope is steep, e.g. a cliff

When equipotential lines are close together, they indicate a strong electric field.

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# Now let’s put these ideas into practice:

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## Learning Standards

Massachusetts 2016 Science and Technology/Engineering (STE) Standards
HS-PS3-1. Use algebraic expressions and the principle of energy conservation to calculate the change in energy of one component of a system… Identify any transformations from one form of energy to another, including thermal, kinetic, gravitational, magnetic, or electrical energy. {voltage drops shown as an analogy to water pressure drops.}
HS-PS3-2. Develop and use a model to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles and objects or energy stored in fields [e.g. electric fields.]
HS-PS3-5. Develop and use a model of magnetic or electric fields to illustrate the forces and changes in energy between two magnetically or electrically charged objects changing relative position in a magnetic or electric field, respectively.