Objective: To investigate experimentally the concept of the electric field and to map (to represent graphically) some electric field lines for particular configurations of charge.
Background: The electric field intensity is defined as the electrical force per unit of charge, or E = F/q. Theoretically, the electric field is determined by using a positive test charge q and determining the force acting on it at every point in space. The direction of the field is found by the laws of vectors and the rule that tells you whether the force is attractive or repulsive. Since a free charge moves in an electric field by the action of the electric force, then work (W = F * d) is done by the field in moving charges from one point to another (e.g., point a to point b ). To move a positive charge from "b" to "a" against the electric field would require work supplied by an external force. The ratio of the work done, W, to the charge, q, in moving the charge between two points in an electric field is called the potential difference, Vab, between the points: Vab = W/q. If a charge is moved along a path at right angles (i.e., perpendicular) to the field lines, there is no work done (W = 0) since there is no force component along the path. No work means no potential difference from point to point. Hence, the potential is constant along paths perpendicular to field lines. Such paths are called equipotentials. Thus, an electric field set up by charges may be "mapped" by determining the equipotential lines (equipotential surfaces in three dimensions) that exist in the region around the charges. Potential difference is easily read by a voltmeter, whereas the measurement of forces would present numerous experimental problems.
Exercise 1: Measuring Equipotentials
Schematic of apparatus
Introduction: The apparatus consists of a flat board on which is placed a sheet of carbonized conducting paper imprinted with a grid. The sheet has electrode configurations of conducting silver paint which provide an electric field when connected to a battery. The standard electrode configurations provided are two circular dots representing point charges of an electric dipole and two parallel linear electrodes representing a two-dimensional cross section of parallel plates. Place one conducting sheet on the board and connect the conductor wires from the battery terminals to the two electrodes. Make connections to the electrodes with thumbtacks to hold spade lugs in contact with the electrodes. The voltmeter measurements will be made using the Data Studio data acquisition program.
Please do not write on the carbonized conducting paper.
Investigation One - In this investigation you will use a voltage probe to sketch four equipotiential lines for the point charges of an electric dipole. You will then sketch the electric field lines.
Investigation Two - Repeat investigation one for the configuration of parallel plates. Make sure you disconnect the battery after finishing Investigation Two.
Exercise 2: Computer-Aided Field Mapping
Introduction: This Physlet enables you to construct a distribution of point charges and then simulate the resulting electric field and potential. Experiment with the simulation and complete the exercises described below.
Procedures and Discussion: Electric Dipole
Add one positive point charge and one negative point charge by clicking once on the buttons. Select and drag the charges into positions that resemble the configuration you explored in the manual mapping exercise. Now check the box that draws field vectors. Note that the field vectors are another way of representing the electric field. The arrow indicates the direction of the field and the color indicates the strength, where black is the strongest and blue is the weakest.
Compare the equipotential and electric field vectors in your simulation to those in your manual map.
Look carefully at the values of the equipotential lines. What is represented by the density of equipotential lines drawn by the applet?
Are the field vectors perpendicular to the equipotiential lines as you assumed for your manual map? Explain why these lines should be perpendicular. Print out a copy of your applet generated map for your lab manual. Refer to the electrostatics lab if you have forgotten how to print an applet.
Obtain a test charge by clicking the "test" button. When the electric field is sufficiently strong, the electric field vector at the position of the test charge is displayed. In addition, when you select and drag the test charge, the electric potential is given at the bottom of the screen. (Caution: the negative sign used in the potential readout is very small.) Explore the field and potential with the test charge. Where is the potential highest and lowest? Where is it zero? Is the electric field zero where the potential is zero? Where is the electric field strongest and weakest? Explain your answer to each question.
Procedures and Discussion: Parallel Plates
De-select the box that draws field lines. Then add an additional positive and negative charge (note, new charges are placed in the same location each time so you must move old charges before you can see the new) and place them very close to the first charges so that the 2 positive charges are aligned parallel to the 2 negative charges. How do the equipotential lines in the new arrangement differ from those in Exercise 1? Now add several more closely-spaced charges to the positive and negative rows in order to simulate a pair of closely-spaced, oppositely-charged parallel plates. Describe the equipotential lines in between the plates. What happens near the edges of the plates? Explain.
Add field vectors to the screen by checking the draw field vectors box. Describe the electric field near the plates.
Use a test charge to explore the
electric potential and the electric field in the vicinity of the plates. What
are the characteristics of these two physical quantities near the plates?
Print out a copy of your applet generated map for your lab manual.
|EField version 4.0 was written by Wolfgang Christian.|