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E01-1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Experiment 1: Equipotential Lines and Electric Fields OBJECTIVES 1. To develop an understanding of electric potential and electric fields 2. To better understand the relationship between equipotentials and electric fields PRE-LAB READING INTRODUCTION Thus far in class we have talked about fields, both gravitational and electric, and how we can use them to understand how objects can interact at a distance. A charge, for example, creates an electric field around it, which can then exert a force on a second charge which enters that field. In this lab we will study another way of thinking about this interaction through electric potentials. The Details: Electric Potential (Voltage) Before discussing electric potential, it is useful to recall the more intuitive concept of potential energy, in particular gravitational potential energy. This energy is associated with a mass’s position in a gravitational field (its height). The potential energy difference between being at two points is defined as the amount of work that must be done to move between them. This then sets the relationship between potential energy and force (and hence field): ! U = U B " U A = " ! F # d ! s A B $ % in 1D ( ) F = " dU dz (1) We earlier defined fields by breaking a two particle interaction, force, into two single particle interactions, the creation of a field and the “feeling” of that field. In the same way, we can define a potential which is created by a particle (gravitational potential is created by mass, electric potential by charge) and which then gives to other particles a potential energy. So, we define electric potential, V , and given the potential can calculate the field: ! V = V B " V A = " ! E # d ! s A B $ % in 1D ( ) E = " dV dz . (2) Noting the similarity between (1) and (2) and recalling that F = q E , the potential energy of a charge in this electric potential must be simply given by U = qV . When thinking about potential it is convenient to think of it as “height” (for gravitational potential in a uniform field, this is nearly precise, since U = mgh and thus 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 AAA-D batteries).
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E01-2 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. 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.
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