# 7.5 Equipotential surfaces and conductors  (Page 5/9)

 Page 5 / 9

Similarly, the charges tend to be denser where the curvature of the surface is greater, as demonstrated by the charge distribution on oddly shaped metal ( [link] ). The surface charge density is higher at locations with a small radius of curvature than at locations with a large radius of curvature.

A practical application of this phenomenon is the lightning rod , which is simply a grounded metal rod with a sharp end pointing upward. As positive charge accumulates in the ground due to a negatively charged cloud overhead, the electric field around the sharp point gets very large. When the field reaches a value of approximately $3.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}\text{N/C}$ (the dielectric strength of the air), the free ions in the air are accelerated to such high energies that their collisions with air molecules actually ionize the molecules. The resulting free electrons in the air then flow through the rod to Earth, thereby neutralizing some of the positive charge. This keeps the electric field between the cloud and the ground from getting large enough to produce a lightning bolt in the region around the rod.

An important application of electric fields and equipotential lines involves the heart. The heart relies on electrical signals to maintain its rhythm. The movement of electrical signals causes the chambers of the heart to contract and relax. When a person has a heart attack, the movement of these electrical signals may be disturbed. An artificial pacemaker and a defibrillator can be used to initiate the rhythm of electrical signals. The equipotential lines around the heart, the thoracic region, and the axis of the heart are useful ways of monitoring the structure and functions of the heart. An electrocardiogram (ECG) measures the small electric signals being generated during the activity of the heart.

Play around with this simulation to move point charges around on the playing field and then view the electric field, voltages, equipotential lines, and more.

## Summary

• An equipotential surface is the collection of points in space that are all at the same potential. Equipotential lines are the two-dimensional representation of equipotential surfaces.
• Equipotential surfaces are always perpendicular to electric field lines.
• Conductors in static equilibrium are equipotential surfaces.
• Topographic maps may be thought of as showing gravitational equipotential lines.

## Conceptual questions

If two points are at the same potential, are there any electric field lines connecting them?

no

Suppose you have a map of equipotential surfaces spaced 1.0 V apart. What do the distances between the surfaces in a particular region tell you about the strength of the $\stackrel{\to }{\text{E}}$ in that region?

Is the electric potential necessarily constant over the surface of a conductor?

No; it might not be at electrostatic equilibrium.

Under electrostatic conditions, the excess charge on a conductor resides on its surface. Does this mean that all of the conduction electrons in a conductor are on the surface?

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