EQUIPOTENTIAL LINES AND FIELD PLOTTING
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1 EQUIPOTENTIAL LINES AND FIELD PLOTTING Marking scheme : Methods & diagrams : 2 Graph plotting : 2 Tables & analysis : 1 Questions & discussion : 3 Performance : 2 Aim: The Preliminary Work section is designed to study the relationships between electric field lines and equipotential lines structures for single charges. The purpose of the experimental section is to investigate the electric field structure between two point charges, between a point charge and a plate and between two parallel plates by identifying their equipotential lines. READ the Preliminary Theory and attempt the questions in that section BEFORE attempting the Preliminary Work section using the electric field applet on the computer (see page 125). Preliminary Theory: The electric field vector E at a point is defined as the magnitude and direction of the force F experienced by a positive charge q at that point. This may be expressed as E = F q. Consequently the units for electric field are Newton/Coulomb (N/C). If a charge of 2µC is in an electric field of strength 3 N/C in the x direction, what is the magnitude and direction of the force experienced by this charge? What can be said about the nature of the electric field about a positive point charge Q? The electric potential energy (PE) at any point is defined as the amount of work that needs to be done in order to move a positive test charge q from infinity (where E = 0) to that point. The electric potential V is then simply defined as that amount of work per Coulomb of charge: V = PE q. Consequently the units for electric potential are Joule/Coulomb (J/C). The derived unit is called Volt (V) in honour of the Italian physicist Alessandro Volta. Another name for the electric potential is voltage. Show that the units for electric field (N/C) are equivalent to Volts/metre (V/m). It is important to note that the electric potential (and electric field) that exists at any point in space can be due not only to the presence of a point charge, but also on the arrangement of any number of charges distributed throughout a region. In addition, electric fields can also result from lines, surfaces and volumes of charge. 38
2 Lines (or surfaces) that join points which have the same electric potential are called equipotential lines or equipotentials. Consequently, no work is done in moving a charge along an equipotential line. This leads to the very important fact that: Electric field lines and equipotential lines (or surfaces) are always perpendicular to each other. What is the shape of the equipotential lines around a point charge? Given that the work done by a force F along a displacement s is W = F s and that the force on a charge q in an electric field E is F = qe, prove that the electric field lines and equipotential lines are always at right angles to one another. Preliminary Work (Computer Simulation): You will need to read the Physics Applets section in the Appendix (on page 116) before attempting the following Preliminary work. Find the positions where the potential is equal to zero for two opposite point charges of equal magnitude separated by a distance of d (Simulation C) and for two equal charges also separated by a distance d (Simulation D). Draw the equipotential and the electric field lines for Simulation F and for Simulation G. Label the zero potential point(s). Experimental Tasks: Draw and label clearly the experimental set-up. In this experiment the voltage divider drawn below will be employed to map out two dimensional equipotential lines for three situations: 1. two point charges, 2. one point charge and a flat plate, and 3. two flat, parallel plates. The magnitude and direction of the electric field lines can then be deduced from these equipotential lines. Before commencing, make sure that the power supply is OFF and that the AMPS button is on low (LO). Now short circuit the + and terminals of the supply by connecting them together momentarily with a lead. Once this is done, switch ON the power supply. The green constant voltage (CV) light should be lit. Turn the coarse voltage knob clockwise until the red light labeled constant current (CC) activates. The green CV light should then go out. If this doesn t happen, you may have to adjust both voltage and current until this occurs. Set the voltage to 20 V ensuring that the red CC light 39
3 remains on. A constant current at a potential of 20 V will be used for the remainder of this experiment. 1. Two point charges Connect the circuit in the previous diagram using only the central bolts on each side of the Teledeltros paper. Use the multimeter to measure the voltage drops across each resistor. Record the results in a table. Are the voltage drops across each resistor exactly the same? Can you explain any differences that exist? The equipotential lines will be detected in the following manner: (i) Place a white sheet of paper on the board and then put carbon paper face down on top of it. (ii) Place the Teledeltros paper on top of them with its black side up. (iii) Insert a bolt at each end to represent the location of the point charges. Tighten the wing nuts onto the Teledeltros paper to form a good electrical connection. It is these wing nuts that will serve as the point charges. The equipotentials can now be located using the probe. Attach one of the leads of the probe at point B (see previous diagram) and the other lead can touch the Teledeltros paper. Search for the spot where a zero reading on the voltmeter is indicated. This spot is therefore at the same potential as point B. Press gently with the probe tip so that the carbon paper can mark this spot with a dot on the white sheet underneath it. Scan across the paper about every 2 cm to find more equipotentials and mark each of these as well. Continue this procedure with the probe lead attached to points C, D, E,... J. You should alternate between dot and cross markers for alternate points for easy identification (ie. 40
4 dots for point B, crosses for point C, dots for point D etc). This should provide nine sets of data. Remove the white sheet and joint the equipotential dots/crosses to form equipotential lines. Any asymmetry in these lines is most likely due to a poor electrical connection between the Teledeltros paper and the wing nut. Note that it will be more efficient if one partner now continues on with the experiment while the other does the measurements and plotting of the graphs. Sketch at least seven electric field lines including the axial one. Remember that the electric field lines intersect the equipotentials at right angles. Plot a graph of the potential versus distance along the straight line joining the two electrodes. In one dimension, the electric field can be written as E = dv dx i. How can you use your graph to calculate the electric field strength at any point between the electrodes? Evaluate the electric field strength half way between the electrodes. 2. Point charge and flat plate Use a fresh sheet of white paper and reuse the carbon paper and Teledeltros paper as earlier. Replace one of the bolts with the copper plate and secure it with the three bolts and wing nuts. If the copper plate looks tarnished, use sandpaper to gently clean the contact surfaces. Attach the power supply lead to the middle wing nut and locate the equipotential lines in the same manner as in section 1. Draw the equipotential lines and sketch at least seven electric field lines. Plot a graph of the potential versus distance along the straight line joining the electrode to the middle of the copper plate. Note your observations of the electric field structure for this configuration. 3. Two flat, parallel plates Again add a fresh sheet of white paper and reuse the carbon and Teledeltros papers. Replace the single electrode with the second flat copper plate and remove any serious tarnish with the sandpaper provided. Connect the power supply leads to the middle wing nuts and detect the equipotentials as before. 41
5 Draw the equipotential lines and sketch at least seven electric field lines. Plot a graph of the potential versus distance along the straight line joining the middle of the copper plates. Note your observations of the electric field structure for this configuration. What can be said about the electric field between two flat, parallel plates? Conclusions: Summarize your results and conclusions from this series of experiments. 42
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