The group has just discovered a large electrically

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Unformatted text preview: ion faithfully reprod uce? What is the specific evid ence? 48 PROBLEM #4: ELECTRIC POTENTIAL FROM A LINE OF CHARGE You work with an astrophysics research group investigating the origin of high-energy particles in the galaxy. The group has just discovered a large electrically charged nebula with an irregular shape. In order to understand how this nebula affects the motion of charged particles passing nearby you must find the electric potential near the nebula. Because of its complicated shape you plan to use a computer simulation. You must determine if the simulation results match the physics you know. You decide to test the simulation for the case of a uniformly charged rod, since the situation is simple enough for direct calculation. You decide to calculate the electric potential at a point a short distance from the middle of the rod along its perpendicular axis, and also at a point a short distance from the end of the rod along its parallel axis. You will then compare these results with those obtained using the computer simulation, to see if the simulation can be trusted. Instructions: Before lab, read the required reading from the textbook and the laboratory in its entirety. In your 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. At the end of lab, disseminate any electronic copies of your results to each member of your group. Read: Tipler & Mosca Chapter 23. Pay particular attention to Sections 23.1, 23.2 & 23.4 and Examples 23-5 & 23-6. EQUIPMENT The computer program EM Field and a ruler. If equipment is missing or broken, submit a problem report by sending an email to [email protected] Include the room number and brief description of the problem. WARM UP 1. Make a picture of the situation. Select an arbitrary point of interest along the perpendicular axis of symmetry. Label relevant distances, angles, and constant quantities. Decide on an appropriate coordinate system. Draw a representative infinitesimal charge element dq somewhere along the rod. 2. Write an expression for the infinitesimal (scalar) electric potential dV produced by dq at an arbitrary point of interest along the perpendicular axis of symmetry. 49 ELECTRIC POTENTIAL FROM A LINE OF CHARGE – 1302Lab2Prob4 3. Write an integral total electric potential at the point of interest in terms of dq. The total electric potential due to a charge distribution is found by calculating the contribution from each charge element to the total (scalar) potential field, and summing the contributions. When the charge distribution is continuous, it may be mathematically divided into infinitesimal elements dq; then the individual contributions are added together with an integral 4 Evaluate the integral you set up in question 3 to obtain an expression for the electric potential at the point of interest. 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. PREDICTION Determine the physics task from the problem statement, and then in one or a few sentences, equations, drawings, and/or graphs, make a clear and concise prediction that solves the task. EXPLORATION In the folder PhysLab on the desktop, open EM Field and click anywhere in the window for the instructions. From the Sources pulldown menu, select 3D point charges. Drag any positive charge to the center of the window of EM Field. From the Field and Potential pull-down menu (shown to the right), select Field vectors. You can reveal electric field by clicking on the locations where you would like the electric field to remain displayed. Look at the Display drop-down menu and explore its options. To place objects at precise points on the screen you can use the ‘show grid’ and ‘constrain to grid’ features from the display pull-down menu. Expand the display window to fill the entire computer screen. Measure the length of the electric field vector at several locations, as well as the distance from the locations to the center of the charged point object. You can remove the displayed vectors using the ‘clean up screen’ option from the Display drop-down menu. 50 ELECTRIC POTENTIAL FROM A LINE OF CHARGE – 1302Lab2Prob4 Try using differe...
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This document was uploaded on 02/23/2014 for the course MANAGMENT 2201 at University of Michigan.

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