PHEN1120-Lab03

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Apr 3, 2024

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PHEN1120 Lab03 Fall 2023 Equipotential Voltage Mapping NAME: Conner Woods, Olivia Whitmore, Sophie Perruffel, Michell Tejera Lab03: EQUIPOTENTIAL VOLTAGE MAPPING INTRODUCTION An electric field is a region in space in which electric forces act on electric charges, if present. The electric field intensity or simply the electric field E, at any point in space is defined as the net electric Coulomb force per unit positive charge acting on a charge q placed at that point. We express this as FE IS the electrical force between charges q and q ’; r is the separation between the charges; the constant k is the Coulomb’s law constant. The SI unit for electric field is N/C (Newton/coulomb), or V/m (volts/meter). The direction of an electric field at any point is defined as the direction of the net electric force on a positive test charge placed at that point. If you hold a small charged particle next to an oppositely charged sphere, it will “fall” towards it. The small, charged particle will be electrically attracted to the sphere, just as a pebble is attracted to the Earth due to the gravitational force. By determining the electric force on a test charge at various points in the vicinity of a charge configuration, the electric field may be ‘mapped’ or represented graphically by lines of force. The English scientist Michael Faraday (1979-1867) introduced the concepts of lines of force as an aid to visualizing the magnitude and direction of the total electric field about a charge or a collection of charges. A line of force is everywhere tangent to the electric field direction. Lines of force originate on positive charges and terminate on negative charges. The density of the lines of force (#lines/cm or # lines /cm 2 ) is a region of space used to represent the electric field strength in that region of space. The electric potential voltage V at point P due to a collection of charges q at a distance r from the point P is defined as The voltage difference between two points separated by the distance d is related to the electric field E as follows: It is possible to find any number of points in an electric field, all of which are at the same electric potential voltage . If a line or surface is constructed (actually or by imagination) such that it includes all such points, the lines or surface is known as an equipotential line or surface. A charge may be moved along such a line or surface without the expenditure of work. Since no work is done in moving a charge along an equipotential surface or line, then the tangential component of the electric force, or the electric field, is zero. The electric field is everywhere perpendicular to the equipotential lines or surfaces. A family of lines drawn perpendicular to the equipotential lines or surfaces describes the shape of the electric field. Mapping equipotential lines is like creating a contour map of a hill in geography. The hill is steepest, and the downhill gravitational force on a ball is greatest, where the lines are close together. A ball placed on a height “contour line” will always roll down in the shortest direction to the next line that is at a lower gravitational 1

Equipotential Mapping Lab 3 potential energy. If we drew a little arrow at each point on the hill to show where a ball will roll, and with what acceleration, we would have a map of the local gravitational field surrounding the hill. In electrostatics, once we have mapped the equipotentials, we can determine the shape of the field surrounding a charged object. The field lines tell us the direction that a “test charge” will travel if it is placed in the field and released. Below (on the left) are diagrams of a geography height contour map and an electrical equipotential voltage map. In this lab, you will map the equipotential for four electrode/charge configurations. Then you will generate an electric field map from these equipotentials. We can easily measure potential differences between points using a voltmeter. Once lines of nearly constant potential (equipotential lines) are known, then the electric field lines can be deduced. Electric field lines are always perpendicular to the equipotential lines, and point in the direction of decreasing voltage. Note the above picture (on the right) of equipotential lines and electric fields of a dipole from Giambattista-Richardson-Richardon 1 ST Ed. We will be generating 2-dimensional equipotential and electric field lines in today’s lab experiment. Objectives  To map the electrical equipotential lines from several standard electrode configurations.  To generate electric field maps from the equipotential lines.  To observe the electrical shielding effects of a closed conductor. EQUIPMENT AND MATERIALS 2

Equipotential Mapping Lab 3  Cork pads,  Thumbtacks,  Conducting paper with painted silver electrodes,  Digital voltmeter.  Digital power supply,  Test leads, alligator clip leads, and banana plug wires, 3

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Equipotential Mapping Lab 3 PROCEDURE 1. Attach one sheet of conducting paper with electrodes to the styrofoam or cork pad by using a thumbtack at each corner. 2. Prepare your voltmeter. Attach a pair of test leads into the COMMON and +DC sockets. Turn the dial on the meter to the 10 V DC setting . 3. Plug in the power supply, but do not turn it on yet. Attach a black alligator + banana plug cable to the negative (-) and another red alligator + banana cable to the plus (+) socket. Do NOT let the free ends of the power leads to touch each other while the power supply is turned on! This will cause a very unpleasant short circuit that may damage the power supply . 4. Identify the silver electrodes on the black paper. You need to connect one electrode to the negative (-) lead, and one to the plus (+) lead coming from the power supply. To do this, connect one end of the hook-up cables (with alligator clips) to a silver thumbtack and press the tack into the foam through the electrode at the locations shown below. The idea is to make a good connection between the thumbtack and the silver electrodes painted onto the paper. (It’s real silver, by the way.) Note that the “electrode” is not just the spot where you insert the thumbtack; the electrode is all of the area of connecting silver. In electrostatic equilibrium, every point on a conductor must be at the same potential! All points on the silver electrode conductor should be at the same potential – you could check this assumption as you do the experiment below. 5. Setup the power supply before you turn it on. Turn both the voltage and current knobs fully counter-clockwise (off). Now turn the current knob a bit clockwise. Turn on the power supply. Turn the voltage knob slowly until the voltage reads 10.0 volts . 6. Take the test leads from the voltmeter into your hands. Touch one lead to each electrode. The voltage should read approximately 10 volts. If you don’t read any voltage, check your electrical connections. If the connections are OK, call the instructor for help. Note that the voltage reading on the power supply should be close to 10V also, but may differ a bit from the voltmeter. The voltmeter is the more accurate readout. 4 Power Supply

Equipotential Mapping Lab 3 7. To map the equipotentials, attach the COMMON lead to the negative electrode. Touch the positive test lead to the black paper. Find several (~5) points at which the potential is 2 V. You should be able to trace a line on the paper with the probe. Once you have found the 2 V equipotential, trace over it with a pencil. Be sure to measure the potentials at points all over the surface of the sheets.  Pattern 1: measure some points between electrodes and behind one of the electrodes 8. Repeat for the other equipotentials at 4V, 6V, and 8V. Make all equipotential lines the same color. 9. Once you have the equipotentials, draw the electric field E lines according to the following rules: a. Electric Field lines are always perpendicular to equipotentials. b. Electric Field lines never cross other field lines. 10. Next Map the other two given electrode configurations.  Pattern 2: measure two voltages curves between the white lines, including a region 5-10 cm beyond the ends. Then continue to measure one voltage curve around behind (outside) one of the white lines. 11. Staple your completed field maps to your lab reports (Divide them up among lab partners so that each partner gets one or two maps) and hand them in with your labs. 5 Pattern 2: Two parallel lines – “Parallel-Plate Capacitor” Pattern 1: Electric Dipole (two opposite point charges)

Equipotential Mapping Lab 3 6

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Equipotential Mapping Lab 3 Summary Questions 1) Pattern 1: a. Where is the straightest equipotential line located? The middle line between the electrodes was the straightest line. This is where the voltage was approximately 5 volts. b. Do the field lines always end at an electric charge (electrode)? The field lines did not always end at the end of the electrode. The field lines extended above and below the electrodes. c. How does your pattern compare to the pattern on page two? Both patterns have electrical fields that are curved at the end. 2) Pattern 2: a. Describe the electric field between the two parallel white lines. The path of the equipotential lines is circular rather than linear as compared to the first pattern. b. Describe the field in the region near the ends of the plates. The field in the region near the ends of the plates should be the strongest equipotential lines in terms of voltage. c. Describe the field in back of the parallel white lines. The field behind the parallel white lines should fluctuate due to the fields morphing around the white parallel lines. 3) In General: a. Are all spots on an electrode equipotential? Why or why not? Yes, there will be lines across the paper where the points along the paper will be equal. b. When the equipotential lines are close together, is the electric field STRONGER or WEAKER than when the lines are far apart? The electric field is stronger when the lines are closer together. c. Did you ever observe equipotential lines crossing each other? No. If the lines crossed each other, the fields would repel each other due to their charge. 7