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MIT 8 02 - Equipotential Lines and Electric Fields

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8.02Experiment 1: Equipotential Lines and Electric FieldsPRE-LAB READINGINTRODUCTIONThe Details: Electric Potential (Voltage)Equipotentials and Electric FieldsNote: Potential vs. Potential DifferenceAPPARATUS1. Conducting Paper Landscapes2. Logger Pro Interface3. Voltage SensorGENERALIZED PROCEDUREEND OF PRE-LAB READINGIN-LAB ACTIVITIESEXPERIMENTAL SETUPMEASUREMENTSPart 1: “Standard” ConfigurationPart 2: “Non-Standard” ConfigurationMASSACHUSETTS INSTITUTE OF TECHNOLOGYDepartment of Physics8.02Experiment 1: Equipotential Lines and Electric FieldsOBJECTIVES 1. To develop an understanding of electric potential and electric fields2. To better understand the relationship between equipotentials and electric fields3. To become familiar with the effect of conductors on equipotentials and E fieldsPRE-LAB READINGINTRODUCTIONThus far in class we have talked about fields, both gravitational and electric, and how wecan 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 whichenters that field. In this lab we will study another way of thinking about this interactionthrough electric potentials.The Details: Electric Potential (Voltage)Before discussing electric potential, it is useful to recall the more intuitive concept ofpotential energy, in particular gravitational potential energy. This energy is associatedwith a mass’s position in a gravitational field (its height). The potential energy differencebetween being at two points is defined as the amount of work that must be done to movebetween them. This then sets the relationship between potential energy and force (andhence field):( )in 1DBB AAdUU U U d FdzΔ = − = − ⋅ ⇒ = −∫F srr(1)We earlier defined fields by breaking a two particle interaction, force, into two singleparticle interactions, the creation of a field and the “feeling” of that field. In the sameway, we can define a potential which is created by a particle (gravitational potential iscreated by mass, electric potential by charge) and which then gives to other particles apotential energy. So, we define electric potential, V, and given the potential can calculatethe field: ( )in 1DBB AAdVV V V d EdzΔ = − = − ⋅ ⇒ = −∫E srr. (2)E06-1Noting the similarity between (1) and (2) and recalling that F = qE, the potential energyof 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 gravitationalpotential in a uniform field, this is nearly precise, since U = mgh and thus thegravitational potential V = gh). Electric potential is measured in Volts, and the word“voltage” is often used interchangeably with “potential.” You are probably familiar withthis terminology from batteries, which maintain fixed potential differences between theirtwo ends (e.g. 9 V in 9 volt batteries, 1.5 V in AAA-D batteries).Equipotentials and Electric FieldsWhen trying to picture a potential landscape, a map of equipotential curves – curvesalong which the potential is equal – can be very helpful. For gravitational potentialsthese maps are called topographic maps. An example is shown in Fig. 1b.Figure 1: Equipotentials. A potential landscape (pictured in 3D in (a)) can berepresented by a series of equipotential lines (b), creating a topographic map of thelandscape. The potential (“height”) is constant along each of the curves.Now consider the relationship between equipotentials and fields. At any point in thepotential landscape, the field points in the direction that a mass would feel a force ifplaced there (or that a positive charge would feel a force for electric potentials andfields). So, place a ball at the top of the hill (near the center of the left set of circles in thetopographic map of Fig. 1b). Which way does it roll? Downhill! But what direction isthat? Perpendicular to the equipotential lines. Why? Equipotential lines are lines ofconstant height, so moving along them at all does not achieve the objective of goingdownhill. So the force (and hence field) must point across them, pushing the objectdownhill. 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 dotproduct of force and displacement. For this to be zero, the force must be perpendicular tothe displacement, that is, force (and hence fields) must be perpendicular to equipotentials.Note: Potential vs. Potential DifferenceNote that in equation (2) we only defined V, the potential difference between two points,and not the potential V. This is because potential is like height – the location we chooseE06-2(a)(b)to call “zero” is completely arbitrary. In this lab we will choose one location to call zero(the “ground”), and measure potentials relative to the potential at that location.E06-3APPARATUS1. Conducting Paper LandscapesTo get a better feeling for what equipotential curves look like and how they are related toelectric field lines, we will measure sets of equipotential curves for several differentpotential landscapes. These landscapes are created on special paper (on which you canmeasure electric potentials) by fixing a potential difference between two conductingshapes on the paper. For reasons that we will discuss later, these conducting shapes arethemselves equipotential surfaces, and their shape and relative position determines theelectric field and potential everywhere in the landscape. One purpose of this lab is todevelop an intuition for how this works. There are four landscapes to choose from (Fig.2), and you will measure equipotentials on two of them (one from Fig. 1a, b and one fromFig. 1c, d).Figure 2 Conducting Paper Landscapes. Each of the four landscapes – the “standard”(a) dipole and (b) parallel plates, and the “non-standard” (c) bent plate and (d) filledplates – consists of two conductors which will be connected to the positive (red) andground (blue) terminals of a battery. In (d) there is an additional conductor which is freeto float to whatever potential is required. The pads are painted on conducting paper witha 1 cm grid.2. Logger Pro InterfaceIn this lab we will use the Logger Pro software and LabPro interface both


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MIT 8 02 - Equipotential Lines and Electric Fields

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