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This write-up is a modified version of the excellent resources available at https://www

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This write-up is a modified version of the excellent resources available at https://www.physicsclassroom.com/. In this lab, we will investigate the electrostatic interaction of charged objects. The electrostatic force between two charged objects is given by Coulomb’s Law: F =K |q1 q2 | r2 (1) where: K = 9 × 109 N·m2 /C2 is Coulomb’s constant. |q| is the magnitude of charge on an object. r is the distance separating the two objects. The force is repulsive for like charges (++ or - -) and attractive for opposite charges (+–). The inverse square dependence on distance means that the force falls off rapidly with separation distance, but never quite goes to zero. A closely related concept is the electric field. A source charge Q will create an electric field whose magnitude is given by: Q E=K 2 (2) r Here: K = 9 × 109 N·m2 /C2 is again Coulomb’s constant. Q is the charge of the source object. r is the distance from Q to the point where you want to evaluate the electric field. The force experienced by a charge q placed within that electric field is simply : F = qE (3) Notice that Eqs. 3 and 2 together recover Eq. 1, as they must. Electric field lines follow simple rules: 1. The direction of the electric field vector indicates the direction of force that would be experienced by a small positive charge placed at that location. 2. Field lines always originate on positive charge and always terminate on negative charge. Either of these charges may be located infinitely far away. 3. Electric field lines are closer together where the electric field strength is largest and further apart where it is weakest. This is a reflection of the 1/r2 nature of the electric field. 4. Electric field lines can never cross, because the electric field must be uniquely defined at each point in space. Crossed lines imply that the electric field points in two different directions at the intersection, and therefore the force experienced by a charge at that location would not be unique. A special electric field line distribution is created by a parallel plate capacitor, as shown in Fig 1. The field within the plates is uniform, points from the positive plate to the negatively charged plate, and has magnitude: Q E = 4πK (4) A where: Figure 1: Electric Field lines of a parallel plate capacitor. K = 9 × 109 N·m2 /C2 is again Coulomb’s constant. Q is the charge on the positive plate. A is the cross sectional area of the plates. Note that the result of Eq. 4 depends on the assumption that the distance separating the two plates is very small. If d is not small, there are significant distortions of the uniform field near the edges of the capacitor. 1 Coulomb’s Law Load the following simulation: http://www.physicsclassroom.com/Physics-Interactives/Static-Electricity/Coulomb-s-Law Click on Launch Interactive. Note that it is a little easier to run this sim if you put it into full screen mode, by clicking the diagonal arrows in the top left corner. Before you record any observations, let’s get a sense of how this all works. Drag the two charged objects about the screen, and observe the direction of the forces acting on each object. The ruler can also be moved and used to determine the separation distance. The major divisions on the ruler are meters, and each grid box is 1 m by 1 m. The sliders can be dragged to change the value of charge on each object, and the charge can be switched from positive to negative on each object with the toggle switches. Finally, note that the value of the electrostatic force between objects is displayed in the upper right of the simulation window. There is nothing for you to record here, but please make sure you don’t move on to the next portion until you have a solid grasp of how the sim works. 1.1 Coulomb’s Law Observations Prepare a table like Table 1 in which you will record your calculations. For each row of Table 1 (except the last) perform the following steps: 1. For the given value of q1 , q2 and r, calculate the electrostatic force given by Eq. 1. Record this in Table 1 as Fcalc . 2. Now set the sim to the values of q1 and q2 . 3. Place the two charges at the horizontal separation distance listed in the current row. q1 (µC) +10 -10 -10 +50 -50 -50 -50 q2 (µC) +200 +200 -200 +600 +600 -600 600 r (m) 6.0 6.0 6.0 9.0 9.0 9.0 Attactive or Repulsive? Fcalc (N) Fsim (N) % diff Table 1: Format for tabulating your observations. 4. Record the simulated value of Force in your table as Fsim . 5. Record whether it is an attractive or repulsive force. 6. Determine the percentage difference between what you calculated and what the sim produced and record it in your table : % diff = ||Fcalc | − |Fsim || × 100 |Fcalc | For the last row of the table, place a charge of -50 µC in the far lower left corner of the simulation grid and a charge of +600 µC in the far upper right corner of the grid, so that they are separated along a long diagonal line. Calculate the separation distance r and enter it into the last line of the table. Fill out the remaining cells in this row as you have done for the previous rows of the table. Your write-up for this section is Table 1 and your numerical work that went into obtaining the values in the table. 1.2 Electric Field Line Observations We will now investigate electric field lines. Load the following simulation: http://www.physicsclassroom.com/Physics-Interactives/Static-Electricity/Electric-Field-Lines Click on Launch Interactive. Note that it is a little easier to run this sim if you put it into full screen mode, by clicking the diagonal arrows in the top left corner. Before you record any observations, let’s get a sense of how this all works. Add + and - charges to the work space and move them about. Drag a charge to the Trash can if no longer needed. Learn to place like charges on top of each other in order to intensify the amount of charge. You can use the Clear Screen button to remove all the charges at once. The simulation shows force vectors in the region of space surrounding a charge or configuration of charges. The strength of these forces is depicted by how bold or how faint the color is. Note: Please make sure you understand the difference between the force vectors shown in this simulation, and electric field lines. They are closely related, but not the same. The simulation force vectors indicate the direction of a force that would be experienced by a positive test charge placed at that point in space. Once you understand how to use the simulation, begin completing the exercises below. 1. The force vectors shown in this simulation can be connected to form unbroken electric field lines. In the sim, create the three configurations of two charges shown in Fig. 2 and observe the electric force vectors. Use these force vectors to guide yourself to draw unbroken electric field lines for each configuration in Fig. 2. You will be handing in your hand-drawn electric field line diagrams. 2. In the sim, create each of the charge configurations of three or more charges shown in Fig. 3. Draw the electric field lines for each situation. Avoid intersecting your electric field lines. Note that Diagram F is similar to Diagram E but has five negative charges piled onto the same location. 3. Compare Diagram E and Diagram F. How does the quantity of charge at a given location seem to affect the curvature of the electric field lines in the space surrounding it? 4. Observe the boldness and faintness of force vectors for any of your configurations. Make a statement describing where the electric field strength is greatest. 5. Use multiple positive and negative charges to create a charge distribution that is similar to a parallel plate capacitor of Figure 1. Of course you can only work in 2 dimensions in this sim, so you will be recreating the side view of a parallel plate capacitor. Draw the field lines as you’ve done in all cases above. What happens to the field lines near the edge of the parallel plates? Your write-up for this section consists of your drawings for Fig. 2 & Fig. 3, along with the written answers to the questions above. Figure 2: Electric Field lines of two charges. Figure 3: Electric Field lines of multiple charges.