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Lab 5: Equipotential Lines THEORY The electric field is the force per unit charge experienced by anything placed in the vicinity of an electrically charged body. It is somewhat similar to the gravitational field, g, which is the force per unit mass experienced by anything placed in the vicinity of another mass. Unlike the gravitational field, the electric field is not equivalent to the acceleration of a freely falling body in the field. If you measured the electrical force acting on a charged body placed in an electric field, then divided that value by the amount of charge on the body, you would have a value for the electric field in Newtons of force per Coulomb of charge. The electric potential is the potential energy per unit charge that anything has at a particular location in an electric field. Lines of equal potential in an electric field are analogous to the contour lines on a topographic map. The "fall line" is perpendicular to those contour lines at any location on a map. The electric field ("line of force") is perpendicular to the lines of equal potential - called equipotentials. Electric potential is measured in Volts, which are equivalent to Joules of energy per Coulomb of charge. A little arithmetic with the units will show that Newtons per Coulomb are very conveniently equal to Volts per meter, so the spacing of equipotentials shows the magnitude of the electric field. Electric field, derived from force, is a vector quantity - it has a direction. Electric potential, derived from energy, is not a vector quantity - it has only a magnitude at a particular location. We are going to explore some two-dimensional electric fields and their associated equipotentials by mapping them. SIMULATION Using the simulation Charges and Fields, simulate the situation shown to the right. This is as close as we can get to a two line electrodes. http://www.colorado.edu/physics/phet/simulations/ chargesandfields/ChargesAndFields.swf Move the equipotential plotter around and.plot a number of equipotential lines with the same ∆V between them. - + - + - + - + - + - + - + Print your results. Repeat for two point electrodes and for one line and one point. In both cases, print your results. Now show examples of each of the following on the diagrams (where they exist): Phys 122 Lab: Equipotential Lines Eyres page 1 rev. 5/09 • • • • A very steep section of a “potential hill” A place where the potential is changing very gradually The gravitational equivalent of a below sea-level region. Draw in electric field lines by hand. (You may check them on the computer.) How do the electric field lines relate to the equipotential lines? The simulation together with information from your book should give you enough information to write out a theory section. PROCEDURE “The Real Lab” 1. Place the sheet of black conductive paper with the dipole electrodes (two spots) on the sheet of foam board, and press two pushpins into the electrode-spots. Connect the battery to the pushpins using the clip-leads. Connect the + terminal to one pin and the - terminal to the other. Set the meter to the 0-10 Volt range. Touch the meter probes to the corresponding (+ or -) electrodes. This is the maximum ∆V of the battery. It should be around 6 V. With the negative probe held in place, touch the positive probe to various places on the conductive sheet. You should see readings on the meter between 0.0 and approximately 6 Volts. Now draw a map of the electrode layout in your lab book, using four small squares in your notebook for each larger square printed on the conductive paper (2:1 in each direction). With the negative probe held at the negative electrode, see if you can find a line of points which all have the same potential - say, 1.0 Volts. As you find each point at that potential, transfer its location to your map and label it with the measured potential. You will find that you can conveniently space these points along a continuous curve, a centimeter or so apart, so that they show the shape of the curve. Draw a smooth curve through these dots. This is called an equipotential line since the potential is the same (equal) at all points along its path. Try several other values of equipotentials between 0.0 and 6 Volts, evenly separated in potential, carrying each line as far as you can. Make sure that you have enough values to draw several equipotential lines each an equal ∆V from the other. • • • Looking at the pattern of lines drawn, come up with some general descriptive statements about the shape of these equipotential lines. Imagine that you have a positive test charge on the positive electrode. Along what kinds of paths would this test charge travel if it were attracted along the shortest path toward more and more negative potentials? Starting from the positive electrode on your map, draw a dotted line outward, perpendicular to the equipotentials you just drew, and arriving at the negative electrode. An arrow on this line will show the direction of this electric field line. Draw a few more electric field lines until you get the hang of it. How do these lines compare to the paths the positive test charge would take? Explain. Check your results with your instructor. Phys 122 Lab: Equipotential Lines Eyres page 2 rev. 5/09 • Follow the same procedure for a set of parallel line electrodes. Try measuring several points along the electrodes themselves - what do you find? Describe the shape and spacing of the equipotential lines between the electrodes. What happens to this shape and spacing as you move out from between the electrodes? ANALYSIS Summarize the method to find the equipotential lines. Now show examples of each of the following on the diagrams (where they exist): • A very steep section of a “potential hill” • A place where the potential is changing very gradually • The gravitational equivalent of a below sea-level region. • Draw in electric field lines by hand. Comment on the patterns found for each electrode arrangement. Then summarize any similarities to give a general description of equipotential lines for any electrode arrangement. Compare your “Real Lab” results with the simulation. Explain the relationship between equipotential lines and field lines. Gravitation field lines can be imagined as the direction a ball would roll on a particular terrain, say from the top of a mountain, or into a hole. If you replaced the positive test charge with a ball, what kind of terrain would give the ball the same motion as the test charge? Describe the terrain for each of the electrode arrangements that you did. CONCLUSION Summarize your findings for equipotential lines and field lines for each electrode arrangement. Be sure to compare to theory. Phys 122 Lab: Equipotential Lines Eyres page 3 rev. 5/09