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Equipotential Lines and Electric Fields Plotting the Electric Field Physics Equipotential Lines and Electric Fields Plotting the Electric Field MATERIALS AND RESOURCES ABOUT THIS LESSON EACH GROUP TEACHER he electrical field produces a force that acts S E 5 alligator clip leads wire cutter between two charges in the same way that G the gravitational field force acts between A 2 batteries, 9 V wire, copper, T P two masses. In this activity students will measure #16 gauge 2 binder clips, large potentials that exist between charged regions, then plot R computer electric fields which are implied by these differences E H ® in potential. LabQuest C A multimeter, OBJECTIVES E seven-function T picture frame, Students will: plastic box-style, • Investigate the space between a pair of electrodes 8.5 in. × 11 in. that are connected to a source of direct current sensor, voltage probe • Plot and examine the plot in terms of the implied ruler, clear metric electric field tape, masking LEVEL 2 pieces wires, copper, #16 gauge, Physics approx. 20 cm Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. i Physics – Equipotential Lines and Electric Fields COMMON CORE STATE STANDARDS (MATH) A-CED.2 (LITERACY) W.3 Create equations in two or more variables to Write narratives to develop real or imagined represent relationships between quantities; graph experiences or events using effective technique, equations on coordinate axes with labels and scales. well-chosen details, and well-structured event sequences. (MATH) S-ID.6B Represent data on two quantitative variables on (MATH) A-CED.4 a scatter plot, and describe how the variables are Rearrange formulas to highlight a quantity of related. Informally assess the fit of a function by interest, using the same reasoning as in solving plotting and analyzing residuals. equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. (LITERACY) RST.9-10.3 Follow precisely a multistep procedure when (MATH) F-LE.2 carrying out experiments, taking measurements, or Construct linear and exponential functions, including performing technical tasks, attending to special cases arithmetic and geometric sequences, given a graph, or exceptions defined in the text. a description of a relationship, or two input-output pairs (include reading these from a table). S (LITERACY) RST.9-10.7 E (MATH) F-LE.5 Translate quantitative or technical information G expressed in words in a text into visual form (e.g., Interpret expressions for functions in terms of the A P a table or chart) and translate information expressed situation they model. Interpret the parameters in a visually or mathematically (e.g., in an equation) into linear or exponential function in terms of a context. R words. E (MATH) N-Q.1 H (LITERACY) RST.9-10.10 Use units as a way to understand problems and to C guide the solution of multi-step problems; choose A By the end of grade 10, read and comprehend E science/technical texts in the grades 9-10 text and interpret units consistently in formulas; choose T complexity band independently and proficiently. and interpret the scale and the origin in graphs and data displays. (LITERACY) W.1 Write arguments to support claims in an analysis of (MATH) S-ID.6A substantive topics or texts, using valid reasoning and Represent data on two quantitative variables on relevant and sufficient evidence. a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted (LITERACY) W.4 to data to solve problems in the context of the data. Produce clear and coherent writing in which the Use given functions or choose a function suggested development, organization, and style are appropriate by the context. Emphasize linear, quadratic, and to task, purpose, and audience. exponential models. v. 2.0, 2.0 Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. ii Physics – Equipotential Lines and Electric Fields ASSESSMENTS NEXT GENERATION SCIENCE STANDARDS The following types of formative assessments are embedded in this lesson: • Assessment of prior knowledge i i • Guided questions DEVELOPING AND ANALYZING AND OBTAINING/EVALUATING • Assessments of Process Skills USING MODELS INTERPRETING DATA COMMUNICATING The following additional assessments are located on our website: • Physics Assessment: Electrostatics • 2010 Physics Posttest, Free Response CAUSE AND EFFECT ENERGY AND MATTER PATTERNS Question 2; 2008 Physics Posttest, Free Response Question 3; Physics Posttest, Free Response Question 2. ACKNOWLEDGEMENTS PS2: FORCES PS3: ENERGY PS4: WAVES S AND INTERACTION Microsoft® product screenshots reprinted with E G ® permission from Microsoft Corporation. Microsoft , A Windows®, and Excel® are either registered P trademarks or trademarks of Microsoft Corporation R in the United States and/or other countries. E H ® ® EasyData™, Graphical Analysis , LabPro , C LabQuest™, and Logger Pro 3® used with A permission, Vernier Software & Technology. E T Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. iii Physics – Equipotential Lines and Electric Fields TEACHING SUGGESTIONS he concept of electric fields was introduced When the circuit is connected, chemical reactions by Michael Faraday. The electric field is will also start that will corrode the tips of the copper Tthe region where the force on one charge wire and will change the resistance, and thus will is caused by the presence of another charge. The also distort the shape of the field if left too long. electric field is a vector quantity and by convention, After each period, the copper wires should be electric fields emanate from positive charges and cleaned with sandpaper or scraped clean. The plastic terminate on negative charges (Figure A). frames should be cleaned after each class period to avoid a build-up of copper compounds. The most likely chemical reactions are • Cu → Cu+2 + 2e− − −2 • H2O + 2e → H2 + O −2 −2 • CO2 + O → CO3 +2 −2 • Cu + CO3 → CuCO3 • H2O (s), a light blue precipitate S Figure A. Electric field There is also a science literacy piece that E accompanies this lesson which requires students to G Plastic picture frames are available from retail stores A interpret the soundness of articles written about the P in either 8 in. × 10 in. or 8.5 in. × 11 in. sizes. These dangers of electromagnetic fields. frames consist of a plastic box with a cardboard R E back for holding pictures. The box makes a good H flat container for holding a thin film of water. The C picture frames should be kept as level as possible so A that the electric field does not appear distorted. The E T water level should be kept shallow, just covering the bottom of the frame completely. Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. iv DATA AND OBSERVATIONS ANSWER KEY Copyright ©2013 National Math +Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. Figure A. Equipotential lines,pointprobe Physics – Equipotential LinesandElectricFields –Equipotential Physics v T E A C H E R P A G E S ANSWER KEY (CONTINUED) Copyright ©2013 National Math +Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. Figure B. Equipotential lines,parallelline probe Physics – Equipotential LinesandElectricFields –Equipotential Physics vi T E A C H E R P A G E S Physics – Equipotential Lines and Electric Fields ANSWER KEY (CONTINUED) ANALYSIS 1. The electric field is constant on the straight 2. For example, choose two equipotential lines, line between the two charges. The electric field one at 10 V and 0.04 m from the positive is not constant along the curved electric field terminal and one at 2 V and 0.06 m from the lines. positive terminal. The electric field between them can be approximated as Electric field lines Equipotential V 10V− 2V lines E == =400 V/m = 400 N/C d 0.06m− 0.04m Notice that the units V/m are equivalent to force per unit of charge, newtons per coulomb (N/C). Figure C. Equipotential and electric field lines, point source S Table 1. Calculating Electric Field Strength E G Line Contact Points Voltage (V) Distance (m) Electric Field (V/m) A 1 A to C 8 − 4 = 4 0.039 100 P R 2 B to D 6 − 2 = 4 0.046 90 E H C 3 C to D 4 − 2 = 2 0.021 100 A E 4 A to G 8 − (−4) = 12 0.107 110 T 5 C to I 4 − (−8) = 12 0.127 90 3. The electric field between the point charges _ varies depending on the distance from + each charged point, becoming weaker with increasing distance. The electric field between the parallel lines is relatively constant. Figure D. Equipotential and electric field lines, parallel lines Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. vii Physics – Equipotential Lines and Electric Fields ANSWER KEY (CONTINUED) CONCLUSION QUESTIONS 1. An electric field is a region in space where one 4. a. The work along an electric field line depends charge experiences a force from another charge. on the magnitude of the charge and the Electric potential is the amount of energy potential difference through which the charge stored in an electric charge due to its position is moved. in an electric field. The strength of an electric b. No work is required to move a charge along field is directly related to the magnitude of the an equipotential line because no force is electric charge producing the field. required, and there is no change in potential. 2. Electric field lines begin on positive charges 5.
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