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Unformatted text preview: s the gravitational potential V = gh). Electric potential is measured in Volts, and the word “voltage” is often used interchangeably with “potential.” You are probably familiar with this terminology from batteries, which maintain fixed potential differences between their two ends (e.g. 9 V in 9 volt batteries, 1.5 V in AAAD batteries). E011 Equipotentials and Electric Fields When trying to picture a potential landscape, a map of equipotential curves – curves along which the potential is equal – can be very helpful. For gravitational potentials these maps are called topographic maps. An example is shown on the right below. (a) (b) Figure 1: Equipotentials. A potential landscape (pictured in 3D in (a)) can be represented by a series of equipotential lines (b), creating a topographic map of the landscape. The potential (“height”) is constant along each of the curves. Now consider the relationship between equipotentials and fields. At any point in the potential landscape, the field points in the direction that a mass would feel a force if placed there (or that a positive charge would feel a force for electric potentials and fields). So, place a ball at the top of the hill (near the center of the left set of circles in the topographic map of Fig. 1b). Which way does it roll? Downhill! But what direction is that? Perpendicular to the equipotential lines. Why? Equipotential lines are lines of constant height, so moving along them at all does not achieve the objective of going downhill. So the force (and hence field) must point across them, pushing the object downhill. But why exactly perpendicular? Work done on an object changes its potential, so it can take no work to move along an equipotential line. Work is given by the dot product of force and displacement. For this to be zero, the force must be perpendicular to the displacement, that is, force (and hence fields) must be perpendicular to equipotentials. Note: Potential vs. Potential Difference Note that in equation (2) we only defined ΔV, the pote...
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This note was uploaded on 09/20/2010 for the course PHYSICS 8.02 taught by Professor Stephans during the Fall '10 term at Rappahannock Community College.
 Fall '10
 Stephans
 Electric Fields, Electric Potential, Mass

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