PHY 212 Laboratory for 1/27/04

Following the instructions provided with the Overbeck Field Mapping Apparatus, each group will map the equipotential lines of two patterns: the Point-Plane and the Faraday Pail patterns. For the Point-Plane pattern, use the 1-volt intervals provided by the apparatus. For the Faraday Pail pattern, use ¹/₂-volt intervals by using the voltmeter in conjuction with the apparatus. Your instructor will demonstrate the method.

Record points close enough together to insure that an accurate equipotential line can be sketched through the points. (In the regions near the conductors, where the direction is changing quickly, spacing should be about one centimeter. It may be about twice that in areas well away from the conductors.) Each member of the group will sketch their own lines, hence each member should have their own copy of the point maps.

Report:

1. Sketch the equipotential lines and indicate the potential of each. Sketch the electric field lines of force for each map. Take care in making your sketch! When drawing the lines of force, remember:
   • The lines of force should be perpendicular to conductors.
   • The lines of force should be perpendicular to the equipotential lines at all points of intersection.
   • The spacing of the lines should reflect the strength of the field. Ideally, if you mark evenly spaced points along a potential line in a region where the field strength is reasonably constant (that means the spacing between the equipotential lines is also reasonably constant), then you should be able to create the field lines by moving your pencil from the marks, staying perpendicular to the equipotential lines. In practice, you will need to make adjustments as you draw. The general rule is: the spacing of the field lines should be proportional to the spacing of the equipotential lines in the nearby region.
   

2. On the point-plane map, select and label two points. The points should lie along one of the electric field lines -- near the point conductor and where the field line intersects adjacent equipotential lines. Estimate the average strength of the electric field between those points using the expression for a uniform field, DV = Ed.

3. Determine the approximate charge residing on the point conductor. This can be done by utilizing the estimated value of E near the point conductor and using the Coulomb expression for the electric field of a point charge. Explain why this represents only an estimate. (Discuss the equations that are used for this estimate.)

4. By noting the spacing between the lines of the electric field you have sketched, show in detail (in a separate sketch) how the charge is most likely distributed on the conducting surfaces of the Faraday pail map. (The last question below is related to this subject.)

5. Answer the following questions:
   1. Why must the lines of force be perpendicular to the surface of any conductor with a static charge distribution?
   2. Is it possible for equipotential lines to cross? Is it possible for lines of force to cross? Explain.
   3. For the Point-Plane pattern, by approximately what percentage does the field strength differ between the region near the point and the region near the plane? Explain your estimate.
   4. For the Faraday pail pattern, comment on the field strength inside the pail. What does this say about the charge distribution on the pail? (Recall your conclusions about the charge distribution on the hollow sphere in the previous static electricity experiment.)