PURPOSE The purpose of this laboratory is to measure the electric potential and determine the electric field strengths between points in electric fields: 1. setup by parallel planes (e.g., a parallel plate capacitor), 2. setup by two physically separated point charges. EQUIPMENT The laboratory requires use ofthe simulation found at https:/fphet. colorado.edwSims html charoes-and- feldsfatest/charges-and-fields en himl REVIEW OF SOME THEORY ON FIELDS Parallel plate capacitors The electric field in the gap between uniformly charged parallel plates is perpendicular to the plates (the electric field is a vector denoted E ). This electric field has strength = | E|. The field strength is related to the voltage across the plates of a capacitor by V=Ed 0 where I is the voltage across the plates (Le., the voltage of one plate with respect to the other), is the strength of the electric field in the gap between the plates and o is the length of the gap (i.e., the distance between the two parallel plates). Therefore v = 2 E (2) which means the electric field strength is proportional to the voltage across the plates of the capacitor, Point harge (or uniformly charged sphere) Due to the shell theorem, it is known that a uniformly charged sphere produces exactly the same electric field at all points outside its radius as would the same amount of charge concentrated at the center of the sphere. Coulomb's law, in conjunction with the shell theorem, shows that the electric field lines set up by a sphere that is uniformly charged with positive charge have direction directly outward from the center of the sphere. The strength of the electric field a distance r from the center of the sphere is given by Coulomb's law, which 15 =2 3) 2 r where E is the strength of the electric field at any point a distance r from the center of the sphere, k1sthe 2 constant .99x10% N and (15 the amount of positive charge on the uniformly charged sphere. c! The electric potential of point A with respect to point B in an electric field set up by a single sphere uniformly charged with positive charge is given by Charting the electric potential and electric field between parallel plates (parallel lines of charges) OBJECTIVE In this section of the laboratory the task is to chart the electric potential and electric field between a simulation of uniformly charged parallel plates. Charting an electric field involves plotting both the equipotential contours and the electric field lines. In this experiment the equipotential contours are found by measurements and sketched in the laboratory notebook. The electric field lines are then found by freehand drawing lines perpendicular to the equipotential contours. PROCEDURE 1. Ina browser, load the simulation found at htips://phet.colorado.edu/sims/html/charges-and- fields/latest/charges-and-fields en.html Sensors Charges and Fields When using the simulation you need to be aware of the following: + the white eraser button in the voltmeter erases all the equipotential contours, not just the one where the voltmeter is positioned, the circular orange "reset/undo\" button in the bottom right corner completely resets the simulation, removing all the charges. 2. In the upper right corner, uncheck the Electric Field box and check the Grid box. 7 10, E E + * + * a YTTELLE; Repeat steps 5 and 6 to find the locations along v = 150 cm, and draw the equipotential contours, for voltages of =100, =50, 0, +50, +100, and +150 V. You will likely have different uncertainties for each of the voltages. Rather than drawing the contours by hand, it s acceptable to take a screenshot that shows all the equipotential contours and thew values. To show the values of the contours, click the Values checkbox. You can click and drag the voltage values so that they don't overlap. Put the voltmeter and tape measure back in the \"storage area\" at the night. Remembering that the direction of the force of a conservative field 1s perpendicular to the energy contows, draw the electric field line that starts at the y= 150 cm position on the line of posiive charges and show where it ends on the line of negative charges. Check the Electric Field box and draw a few more electric field lines in the region between the two lines of charges. Pay particular attention to the field lines near the edpes of the lines of charges. Onee you have checked the Electric Field box, it is acceptable to take a screenshot and use that m your report rather than drawing the electric field lines by hand. 3. Click and drag the positive and negative I nC charges so that they are arranged in two parallel lines of 16 charges each, separated by 300 cm. Note that each major square of the grid is 50 cm x 50 cm, and the small squares are 10 cm x 10 cm. Each line of charges should be 300 cm long: 1004000 000 00 00000 O 300 2 er 4. Draw the grid and the arrangement of charges in your laboratory notebook, using an appropriate scale. Let the bottom left positive charge define the origin of an x-y coordinate system. It is also acceptable to take a screenshot of the initial setup. 5. Move the Equipotential tool (a voltmeter) along the horizontal line at y = 150 cm until it reads a voltage of a close as possible to -150 V. However close you can get, use that as the uncertainty in the voltage. For example, suppose that the closest you can get is -150.6 V. Then record the voltage as -150.0 +0.6 V. Use the tape measure to record the x coordinate of this position. Remember to record the experimental uncertainty of this position. Hint: Be reasonable in estimating the uncertainty. Even though the tape measure reads to the nearest 0. I cm, is your ability to position and align the tape measure this precise? In other words, your position uncertainty will be greater than 10.1 cm. O -HITY 6. Click the pencil icon on the voltmeter. The green contour line that appears shows all the locations where the voltage is -150 V. Carefully draw this equipotential contour line in your notebook and label its voltage. Remember that the white eraser button in the voltmeter erases all the equipotential contours, not just the one where the voltmeter is positioned