Physics 241 Lab Electric Field Mapping Overview: This lab is very straightforward and helps tie the ideas of electric field and electric potential together. You will be finding the electric fields created by various distributions of charge on a 2-dimensional sheet of conductive paper. You learning objectives are: • To understand the conceptual connection between electric potential and electric field. • To understand the mathematical connection between electric potential and electric field: ! "V =r E • dr s # and r E =$%V%xˆ x ,$%V%yˆ y ,$%V%zˆ z & ' ( ) * + . • To learn how to approximate a derivative with finite-sized measurements: ! "#V#x$"%V%x. Introductory Discussion: 1. ENERGY LANDSCAPE: U(x,y) mountain analogy. The U(x,y) mountain is created by a positive charge on the top with Styrofoam examples. Steepness of mountain gives direction and strength of force on a small positive test charge down the U(x,y) mountain. 2. ENERGY LANDSCAPE PER UNIT CHARGE: V(x,y) mountain analogy. The V(x,y) mountain is created by a positive charge on the top with Styrofoam examples. Steepness of mountain gives direction and strength of Electric Field down the V(x,y) mountain. 3. Math relating “steepness” concept to “negative slope/derivative” math operation. o 1-D potential, V(x). o 2-D potential, V(x,y) (Cartesian coordinates then polar coordinates for central potential) 4. Math relating ! r F and U using slope compared to ! r E and V … it’s the same math! 5. How to approximate a derivative in the lab. 6. Example problem of sketching electric field lines using equipotentials. (SEE FIRST EXAMPLE) 7. Example of how to find the x AND y component of the electric field at a point, ! Ex(xo, yo) and ! Ey(xo, yo). (SEE FIRST EXAMPLE) 8. Example problem of plotting graph of V(x,y) along a line of symmetry. (SEE SECOND EXAMPLE) 9. Example problem of calculating and plotting ! r E along line of symmetry using your graph of V(x,y) along the same line of symmetry. (SEE FIRST EXAMPLE) 10. DEMO: Hook up parallel plate conductive paper with 10 Volts of potential difference. 11. DEMO: Map many points of 7 Volts to be able to sketch the line of 7 Volts equipotential.Some people find the above picture useful for connecting the various electrostatic concepts together and even add to it as they learn more.Worksheet: 1. In the following picture depicting equipotential lines (dashed lines of constant voltage), sketch the corresponding electric field lines (draw the electric field lines with solid lines). Be sure to label the direction of the electric field lines using arrows using the assumption that VOUT < VIN. [Draw in the picture.] 2. In the following picture assume VOUT < VIN. Describe how each of the two test charges shown would move if placed where shown. [Draw in the picture and write an explanation beside the picture.]3. In the following picture depicting equipotential lines (dashed lines of constant voltage), label the two regions that have the strongest electric field and the two regions that have the weakest electric field. Next to the picture, explain how you made your decision. [Draw in the picture and write an explanation beside the picture.] 4. In the following picture depicting labeled equipotential lines, calculate the electric field at the marked point in space using the derivative approximation. Be sure to find EX and EY, and write your final answer in vector notation. [Show your calculations in the space next to the picture.]5. Use the dipole conductive paper (two dots) and plot at least 7 dashed equipotential lines on the supplied field mapping paper. [Make a copy for both lab partners.] 6. Sketch at least 8 electric field lines using solid lines on top of the dashed equipotential lines you just graphed. 7. Label the part of your sketch where the electric field appears to be the strongest. 8. Choose a point of low symmetry on your field mapping paper and calculate the electric field at that point using the derivative approximation. The coordinates for the point chosen were: ( ____________ , ____________ ) The electric field calculated there was ! r E = ___________ ! ˆ x + ____________ ! ˆ y 9. Draw both electric field components for the point in the previous problem as arrows on your field mapping paper and label the strength of the field in each direction. At this point your field mapping paper should look something like this only with many more lines: 10. On regular graph paper, graph V(x,0) along the line of symmetry that goes through both poles of the dipole. (SEE EXAMPLE). 11. On another sheet of regular graph paper, use the derivative approximation to calculate and graph EX(x,0) between pairs of V(x,0) points. This requires calculating the electric field in the x-direction only for points along the line of symmetry. (SEE EXAMPLE).12. Below is a sketch of some equipotential lines (dashed) and some field lines (solid). The points where these intersect are labeled. If an electron is released from rest at point e, which intersection will it reach some time later? Explain your reasoning. Now find the velocity of that electron when it reaches that point. Hint: work from an energy perspective with ! "K = #"U = # q"V( )= # #e"V( ) where ! K =12mv2. Note: me = 9.1x10-31 kg. [Write your explanations and work next to the picture.] 13. (Authentic Assessment: 2 points) You are given a strip of conductive paper electrified with a AAA battery. You need to determine the average electric field inside the strip (including direction). YOUR SCORE: ___________________14. (Open-ended question / creative lab design) Use the cathode ray tube conductive paper to find out what happens when a positive test charge of +3.0 Coulombs is placed at three unique locations on the paper (points A, B, and C given in picture below). I expect you to use the equation ! r F E= qr E to calculate the magnitude of the acceleration of the test charge if its mass is 10 g. In the area below and on additional paper if necessary, design an experiment to find the initial accelerations of the +3 Coulomb charge when placed in each of the three locations (assume it is initially stationary). Then implement your experiment and make your observations. You may “cheat” by talking to other groups for ideas, but not “cheat” by already knowing the answer or looking it up. 15. You
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