Lab_2_ClaraM

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Dec 6, 2023

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Lab 2: Charges, Fields and Potential Lines Answer all the questions directly on this document. 1. Play with the simulation (Charges and Fields) and get oriented with all of the different options. This should help you understand the lab better. Activity 1 2. From the box at the bottom of the screen, drag a red +1 nC charge into the middle of the screen. 3. If not already selected: Select ‘Electric Field’. How does the brightness of the arrow relate to the strength of the field? What happens when you check/uncheck ‘Direction only’? Which way do the arrows point for a positive charge? The arrow is brighter towards the center of the positive charge and gets dimmer as it goes further. When you uncheck direction only the arrows go from brighter to dimmer, when you check it all the arrows are present and bright. The arrows point away from the positive charge. 4. Drag the red +1 nC charge back into the box at the bottom, and then drag a blue – 1 nC charge onto the screen. Which way do the electric field arrows point for a negative charge? They point towards the negative charge. 5. Click on the yellow Sensor at the bottom and drag it across the electric field. What information do the Sensors show? The sensor shows an arrow pointing towards the charge showing the magnitude and direction of the electric field. 6. What happens to the electric field as you move further from the charges? The electric field gets weaker. 7. Take the blue Voltage meter (labeled ‘0.0 V’). What information does the voltmeter give? What information is given when you click on the pencil (you should have a green circle)? What does the green circle represent? (If you’re not sure, move on and come back to this later.) The voltmeter gives us electric potential. The pencil will give a circle around the charge with the voltage. It represents the range of the voltage around the negative or positive charge. Activity 2 (If you want to reset the screen, click on the orange circle arrow in the bottom right corner. Do this before each activity) 8. How can you make a charge of +2q? How can you make a charge of -3q? By dragging the appropriate number of charges toward the middle. 2 positives for +2q and 3 negatives for -3q. 9. Determine what charges (magnitude and positive/negative) would give you the electric field lines shown below? (You may need to try different combinations to determine the magnitudes of each charge.) Left is positive (+1nC) and right is negative (-1nc).

10. When you have two opposite but equal magnitude charges along a horizontal line (similar to the picture above), where is the electric field the greatest? Is there ever a point where the field will be zero? The electric field is greatest when its closest to the charge. Yes, when its away from the charge. 11. When you have two of the same charges along a horizontal line, where is the electric field the greatest? Is there ever a point where the field will be zero? The electric field is greatest when closest to the charge. Yes, it is zero when it moves furthest away. 12. Determine what charge/charges (magnitude and positive/negative) would give each the lines of equipotential shown below? (For each situation, turn the ‘ Electric Field ’ on and off to see how the electric field lines compare to the equipotential lines) a) b) +1 nC charge -1 nC charge

c) -1 nC charge on left (2), +1 nC charge on right (2) d) +1 nC charge on left (3), +1 nC charge on right (3) 13. When you have two opposite but equal magnitude charges along a horizontal line (similar to the picture above), where is the potential the greatest? Is there ever a point where the potential will be zero? The potential is greatest at the point charges and zero at the center. 14. When you have two of the same charges along a horizontal line, where is the potential the greatest? Is there ever a point where the potential will be zero? The potential is greatest at the point charges and there is no point where the potential will be zero.

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Activity 3 15. Make a long vertical line of positive charges by placing them very close together , similar to what’s shown to the right. How does the electric field change as you move around the line of charges? Moving around the line of charges the electric field stays the same. If you move further away from this line, it decreases. However, close to the line the electric field is at its greatest. 16. Make a long vertical line of negative charges 2 meter from the positive charges similar to what’s shown below. This is your parallel-plate capacitor. How does the strength of the electric field change between the two lines? How does the direction of the electric field change between the two plates? The electric field weakens as you move from the positive plate to the negative plate. The electric field's direction is always going to be from the positive plate to the negative plate. 17. Place sensors at 3 different locations between the lines to get readings of the electric field, each at different distances from the lines. 18. Use the voltmeter to draw lines of equal potential at the locations of the three sensors by clicking on the pencil button on the voltmeter. When you have the voltmeter at each distance, click this button. Doing so will record the potential V and draw a green line on the screen. Include a screenshot of your capacitor with 3 sensors and 3 green lines/circles.

19. Fill in the table below for each of the locations. (In order to see the potentials, you may need to move the sensors.) Location Distance from positive plate (m) Electric field E (V/m) Potential V (V) 1 0.321 m 181.59 58.29 V 2 0.75 m -13.97 -10.48 V 3 4.68 m -0.90 -4.200 V Activity 4 20. Place six +1 nC charges on top of each other somewhere on the left side of the screen. (It can go anywhere, but there needs to be enough space to measure 8 m away.) 21. From the box at the bottom, drag a Sensor and place it 1 m to the right of your charge. This sensor measures the E field at the location of its placing. In the table at right, record the E field magnitude at a distance r of 1 m. Ignore the degrees. 22. Drag the Sensor to the other distances shown in the table, then record the E field measurements. 23. Drag your Sensor back and replace it in the box at the bottom of the screen. 24. Using the voltmeter, record the potential V by drawing a green line on the screen at each distance. Fill in the table at the far right. Include a screenshot with all of the green circles. r (m) E (V/m) 1 53.92 2 13.5 3 6.0 4 3.38 5 2.17 6 1.50 7 1.11 8 0.85 r (m) V (V) 1 52.1 2 25.8 3 17.5 4 13.3 5 10.6 6 8.9 7 7.7 8 6.7

25. Write the equation for the electric field at any distance r from a point charge q : E= kq/r^2 26. Write the equation for the potential at any distance r from a point charge q : V=kq/r 27. Using the table above, make a graph in Excel of electric field E and distance r to determine Coulomb’s constant k using the appropriate trendline. Hint: In Excel your trendline will not be straight – the equation for E(r) is not linear. You must ask Excel to apply a power trendline appropriate to your equation. This is called “curve fitting”. What power would you expect based on the equation? 28. Insert the graph below and write down the k value that you found. Compare this value to the accepted value. Report your error as follows: |Experimental value – Accepted value| × 100% = your percent error |Accepted value| [(8.9755*10^9 – 8.99 *10^9) / (8.99 * 10^9)] x 100% = 0.16% 29. Using the table above, make a graph in Excel of voltage V and distance r to determine the constant k again using the appropriate trendline. (The same hint as above applies, but the work will be slightly different because the equation is different.) 30. Insert the graph below and write down the k value that you found. Compare this value to the known value using percent error/difference? [(8.6035*10^9 – 8.99 *10^9) / (8.99 * 10^9)] x 100% = 4.30% 31. Remove the charges and place a positive charge in the center of the grid. Draw five equipotential circles with the potentials of 10 Volts, 8 Volts, 6 Volts, 4 Volts and 2 Volts. (It might be hard to get the precise values but try to get as close as you can).

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Take an electric field sensor and move it in a straight line, crossing the equipotential lines. Describe the relationship between the distance between the equipotential lines and the strength of the electric field. When moving the electric field sensor, it was clear that the closer the equipotential lines were to one another, the stronger the strength of the electric field was. Conclusions: Use the observations above and the concept of work to describe and explain • the relative orientation between the equipotential lines and field lines • the relationship between the direction of the electric field and increase or decrease in potential • the relationship between the magnitude of the electric field and the distance between the pairs of lines with the equal potential difference Electric field lines and equipotential lines are always perpendicular. The electric field lines indicate in the direction of decreasing potential as they move from a higher potential to a lower potential. When the equipotential lines are closer together, the electric field is stronger. The magnitude of the electric field is inversely related to the spacing When you are done, send the completed lab to me as an attachment on Wamap.

Lab_2_ClaraM

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