Physics Lab 202P-3. Electric Fields and Superposition: A Virtual Lab NAME: LAB PARTNERS:

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1 Physics Lab 202P-3 Electric Fields and Superposition: A Virtual Lab NAME: LAB PARTNERS: LAB SECTION: LAB INSTRUCTOR: DATE: ADDRESS: Penn State University Created by nitin samarth Physics Lab 202P-3 Page 1 of 12

2 Physics Lab 202P-3 Equipment List (all items marked with * are in the student kit, others are supplied at the time of the lab) N/A Computer Software List EM Field Microsoft Excel Penn State University Created by nitin samarth Physics Lab 202P-3 Page 2 of 12

3 Prelab checkbox: Satisfactory Unsatisfactory Physics Pre-lab 202P-3 Electric Fields and Superposition Name: Section: Date: (Read this & answer the questions before coming to lab) Summary of relevant concepts: (a) The electric field at any point in space is defined as the force experienced by a test charge of +1 C. Hence, the magnitude of the electric field at a distance r from a SINGLE point charge Q is given by Coulomb's Law: Q E = k 2 r where k = 8.99 x 10 9 N-m 2 /C 2. (b) The electric field from a COLLECTION of POINT charges is given by the vector sum of the electric fields from all the individual point charges ( superposition ). (c) Electric field lines provide a convenient way of visualizing the electric field in any region of space: Electric field lines originate at positive charges and terminate at negative charges; The electric field at any given position is tangential to the electric field line; The spacing between electric field lines is inversely proportional to the strength of the electric field: i.e. they are closer together where the field is stronger, and further apart where the field is weaker. (d) A common arrangement of charges in Nature is the electric dipole. This consists of two charges equal in magnitude Q but of opposite sign, separated by a distance a. An electric dipole is characterized by the dipole moment p= Qa. This is a vector that points from the negative charge towards the positive charge. Penn State University Created by nitin samarth Physics Lab 202P-3 Page 3 of 12

4 Pre-lab Questions: Q1. An important principle that you learnt about in lecture is superposition. The use of superposition depends on a clear understanding of vector sums. What is the vector sum of the three vectors shown below? They all have the same magnitude Magnitude of resultant vector = Direction of resultant vector = Q2. The figure below shows 4 positive charges of equal magnitude arranged on a semicircle centered about the origin. What is the direction of the net electric field produced at the origin? Direction of electric field = y x Penn State University Created by nitin samarth Physics Lab 202P-3 Page 4 of 12

5 Now, use superposition to calculate the direction and magnitude of the electric field at a point P that lies on the perpendicular bisector of an electric dipole. (See figure below.) Your goal is to first determine the electric field at any general value of r, and then in the limit r >> a. P +Q -Q r a Q3. In the diagram above, draw vectors that represent the electric field produced at P by each charge. Also, draw a vector that represents the net electric field produced by the sum of these two vectors. Q4. From the vector diagram that you used above, derive an exact expression for the magnitude of the electric field at P. The only parameters in your final expression should be the dipole moment p = Qa, the distance r, the distance a and the constant k from Coulomb's Law. Call this expression "Equation 1." Penn State University Created by nitin samarth Physics Lab 202P-3 Page 5 of 12

6 Q5. Simplify your analytical expression for E(r) for large distances i.e. r >> a. You should obtain a particularly simple expression. Call this expression "Equation 2." Q6. A rule of thumb calculation (no calculators!). Suppose you are at some distance r from an electric dipole, such that r is much larger than the dipole separation a. You measure the magnitude of the electric field from the dipole to be N/C. If you double your distance from the dipole, approximately what is the magnitude of the electric field? Penn State University Created by nitin samarth Physics Lab 202P-3 Page 6 of 12

7 Lab Activity 1: Electric Field From A Collection of Point Charges In this first activity, we ll use a program called EMFIELD to visualize the electric field created by different arrangements of point charges. Start the EMFIELD from the Physics program group under the START menu. From the "Display" menu, select "Show grid" and "Constrain to grid"; From the "Sources" menu, select "3D point charges"; From the array of positive and negative charges at the bottom of the screen, select appropriate charges and position them to represent the arrangements shown in each question below. From the "Fields and potential" menu, select the "Field vectors" option. When you click at any point on the screen, the program will now show you the electric field vector at that point. Set up the charge arrangement shown in the figure below in which the 8 point charges are arranged on the corners of two concentric squares. The small square has each side roughly half the length of the large square. The x and y axes bisect the sides of the large square and pass through the vertices of the small square as shown. Suppose an electron were released from rest from positions A, B and C. Use the EMFIELD program to solve the questions on the following page. A word of caution: the program makes mistakes in regions where the electric field is very small! Use physical intuition and common sense in interpreting your results! +1 C +1 C -1 C -1 C +1 C A B C +1 C -1 C -1 C Penn State University Created by nitin samarth Physics Lab 202P-3 Page 7 of 12

8 Q1. Using EMFIELD, figure out the DIRECTION and RELATIVE MAGNITUDE of the instantaneous acceleration experienced by the electron when its is released from position A, B and C. In the figure on the previous page, draw vectors that represent these accelerations, with the lengths drawn proportional to the magnitudes. Discuss briefly below how you would answer this question without a program such as EMFIELD. Penn State University Created by nitin samarth Physics Lab 202P-3 Page 8 of 12

9 Lab Activity 2: Modeling the Electric Field of a Water Molecule A very common charge arrangement in Nature is the electric dipole in which two equal but opposite charges Q and Q are separated by a small distance a. Many types of molecules (e.g. water) act like electric dipoles and may be characterized by the "dipole moment" p = Qa. Note that this is a vector which (by definition) points from the negative to the positive charge. A water molecule has zero net charge, but it produces an electric field around it similar to the electric field of a dipole. The figure below shows a model of a water molecule, with the three nuclei represented as black dots and the electron clouds represented as spheres. HYDROGEN Dipole Moment p OXYGEN Q2. Refer to the figure above: explain qualitatively why a water molecule acts like an electric dipole. (Think about the charge distribution in the model above.) Penn State University Created by nitin samarth Physics Lab 202P-3 Page 9 of 12

10 A. Visualizing the electric field from a dipole. Now, we ll use EMFIELD to plot the electric field from a dipole. From the "Sources" menu, select "3D point charges"; From the array of positive and negative charges at the bottom of the screen, select a positive charge and drag it to a position somewhere near the middle of the screen. Select an appropriate negative charge and position it to form a dipole. From the "Fields and potential" menu, select the "Field vectors" option. Q3. Use the program to find out the DIRECTION of the electric field vectors at positions P1, P2, P3 and P4 in the diagram below. Based on your observations, sketch in the figure below arrows that represent the FORCE experienced by a proton at positions P1, P2, P3 and P4. Note that P2 and P4 lie on the perpendicular bisector of the line joining the charges. P4 P1 +Q -Q P3 P2 From the "Fields and potential" menu, select the "Field lines" option. When you click on any point on the screen, you will see an electric field line that passes through that point. You can use this option to construct an electric field line plot for your electric dipole. Note that electric field line plot is only meaningful if you obey the proper rules! Specifically, electric field lines should be closer together where the electric field is stronger, and further apart where the electric field is weaker. Penn State University Created by nitin samarth Physics Lab 202P-3 Page 10 of 12

11 Q4. If you randomly click at any point on the screen, EMField will plot an electric field line passing through that point. So, you could create an electric field line plot by selecting any number of random points on the screen. Try this! Why is the resulting electric field line plot not particularly meaningful? Describe a strategy that will help you make a correct plot of electric field lines. Again, remember the basic rules! Q5. Make a meaningful plot of the electric field lines from an electric dipole. Print out your plot and include it with your lab report. Observe the characteristics of your electric field line plot. Q6. How are the electric field vectors related to the electric field lines? Q7. Do electric field lines ever intersect? Yes No Explain your answer briefly. Penn State University Created by nitin samarth Physics Lab 202P-3 Page 11 of 12

12 B. Numerical Calculation of the Electric Field of a Water Molecule Q8. A good model for the water molecule is to consider it as a dipole with two charges of +10e and 10e, where e is the charge on an electron (since that's the total number of electrons or protons in the molecule). If the dipole moment of the molecule has a magnitude p = 6.2 x C m, what is the separation between the two charges in this model? A numerical calculation is useful to visualize how this dipole field varies with distance. Open the spreadsheet dip.xls in the Movies folder. Q9. Using equation 1 that you derived in the prelab, tabulate the magnitude of the electric field E(r) of the dipole model of a water molecule as a function of r. Plot the electric field versus distance using a log-log scale so that you can easily see the behavior of E(r) over the entire range of distance. Include a hard copy of your table + the plot with your lab report. Explain briefly why it is not convenient to use a standard linear scale in the plot. Q10. Using the plot you just made, determine how large r needs to be for Equation 2 to be accurate. Relate this scale with the dipole parameter a. Penn State University Created by nitin samarth Physics Lab 202P-3 Page 12 of 12