Then work through the exploration measurement

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Unformatted text preview: our lab notebook, respond to the warm up questions and derive a specific prediction for the outcome of the lab. During lab, compare your warm up responses and prediction in your group. Then, work through the exploration, measurement, analysis, and conclusion sections in sequence, keeping a record of your findings in your lab notebook. It is often useful to use Excel to perform data analysis, rather than doing it by hand. A t the end of lab, disseminate any electronic copies of your results to each member of your group. Read : Tipler & Mosca Sections 21.4, 21.5, & 22.1 and Exam ple 22-1. EQUIPMEN T The com puter program EM Field and a ruler. If eq uipment is missing or broken, submit a problem report by sending an email to l . Include the room number and brief description of the p roblem. WARM UP 1. Make a picture of the situation. Select an arbitrary point of interest along the perpend icular axis for calculating the electric field . Label all relevant constant quantities, d istances, and angles. Decid e on an appropriate coord inate system . Draw a re presentative infinitesim al charge elem ent d q som ew here along the rod . 2. Draw an infinitesim al electric field vector d E p rod uced by d q along the perpend icular axis of sym m etry. Write an expression for its m agnitud e. Draw and label its com ponents. Write expressions for each com ponent. 3. Write an integral for each com ponent of the total field at the point of interest in term s of d q. The total electric field d ue to a charge d istribution is fou nd by calculating the 41 THE ELECTRIC FIELD FROM A LINE OF CHARGE – 1302Lab2Prob2 contribution from each charge elem ent to the total (vector) field , and su m m ing the contributions (as vectors). When the charge d istribution is continuous, it m ay be m athem atically d ivid ed into infinitesim al elem ents d q; then (for each field com ponent) the ind ivid ual contributions are ad d ed together w ith an integral. (N ote: Alw ays consid er the sym m etry of the situation. It m ay be that the integral for one of the com ponents vanishes for som e reason. Explore this.) 4 Evaluate the integral(s) you set up in question 3 to get an expression(s) for the electric field ’s com ponents at the point of interest. Write an expression for the total field m agnitud e and ind icate its d irection . In order to evaluate such an integral, all terms in the integrand must be either constants or explicit functions of the integration variable. First, choose an appropriate integration variable. Then, rewrite all variable quantities in the integrand (including dq) in terms of the integration variable you have chosen. Determine appropriate limits for the integration variable you have chosen. Use the Pythagorean Theorem, trigonometry, and the linear charge density to write your integrand(s) in a suitable form. 5. Repeat steps 1-4 for an arbitrary point of interest along the parallel axis. EXPLORATION In the fold er P hysLab o n the d esktop, open EM Field a nd click any w here in the w ind ow for the instructions. From the S ources p ulld ow n m enu, select 3D point charges. Drag a ny positive charge to the center of the w ind ow of EM Field . From the Field and Potential p u ll-d ow n m enu (show n to the r ight), select Field vectors. You can reveal electric field by clicking on the locations w here you w ould like the electric field to rem ain d isplayed . Look at the D isplay d rop -d ow n m enu and explore its options. To place objects at precise points on the screen you can u se the ‘show grid’ a nd ‘constrain to grid’ features from the display p ull-d ow n m enu. Expand the d isplay w ind ow to fill the entire com puter screen. Measure the length of the electric field vector at several locations, as w ell as the d istance from the locations to th e center of the charged point object. You can rem ove the d isplayed vectors using the ‘clean up screen’ o ption from the D isplay d rop -d ow n m enu. Try using d ifferent m agnitud es of charge. What range of charge values allow s you to accurately m easure the length of the electric field vector at all points on the screen? Where is a good place to put the configuration in ord er to get a larger num ber of m easurem ents? 42 THE ELECTRIC FIELD FROM A LINE OF CHARGE – 1302Lab2Prob2 To check w hether or not you get the correct behavior of the electric field from a point charge d o the follow ing: 1. Pick a useful charge value and d eterm ine several locations at d ifferent d istances r from the center of the single point charge. (H int: Choose your locations at regular intervals.) At each location , m easure r a nd the length of the electric field vector. In your notebook, record the d ata and sketch a plot of the vector length as a function of r. 2. N ow , calculate w hat Coulom b’s law pred icts and sketch the values for the field strength vs. d istance (r) on the same graph. 3. Com pare the shape of the graph to that based on the Coulom bs’ law and record your observations. You hav...
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