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UW-Madison PHYSICS 208 - EC-2: Electric Fields and Potentials

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Name________________________________________ Section___________ Question Sheet for Laboratory 4: EC-2: Electric Fields and Potentials OBJECTIVE: To understand the relation between electric fields and electric potential, and how conducting objects can influence electric fields. APPARATUS: 1. Numerical EM simulation applet, and voltage source, electrometer, graphite paper, and potential probes. INTRODUCTION: You use two different ways to investigate electric fields and potential. The first is a real-time digital simulation of electric fields and potentials in vacuum (www.falstad.com/emstatic). It lets you position various charges and conducting objects by dragging and clicking, then calculates the electric field direction and equipotentials for you. It divides space up into discrete blocks to do the calculation, and so is not particularly accurate. The second is a real-time analog simulation of electric potential using a high-resistance (but still conducting) medium to simulate vacuum. Small currents flow through this medium along electric field lines, which generate electric potential variations that you measure with the electrometer. This lets you quantitatively measure electric potentials and calculate electric fields. A. Numerical Simulation (Don’t spend more than 1 hour on part A) Point Firefox at www.falstad.com/emstatic, and start up the applet. It starts up showing the electric field directions and equipotentials from a point charge. Enlarge the window to take up most of the screen, but be careful to preserve the aspect ratio (e.g. so the circular charge is still circular). You should be able to click and drag the positive charge around on the screen. A1. The white line countours are equipotentials, connecting points in space that have the same electric potential. Each contour is a different electric potential, and the electric potential difference between adjacent contours is a constant value ΔV. Why do the equipotentials get farther apart as you move away from the charge?2 A2. Under the setup menu choose “Double Charge”. What is the direction of the electric field midway between the two charges? Where do you think the electric potential is equal to zero? Is the electric potential a local minimum, local maximum, or neither, midway between the two charges? (Hint think about the equipotential countours)3 A5. Under the setup menu choose ‘Dipole’. Click and drag the charges so that the dipole plane is horizontal near the bottom of the screen, and takes up most of the screen. Select ‘Mouse=Add Conductor (Gnd)’ and draw a filled rectangular object near the top of the screen. Select ‘Mouse=Make Floater’ and convert the grounded conductor to a floating conductor by clicking on it. It is now an isolated conductor with approximately zero charge on it. Select ‘Mouse=Move Object’ and drag the conductor around on the screen. The local charge density on the conductor is color coded, blue for negative and yellow for positive. i) Drag the conductor down between the dipole charges. Describe what happens to the charge distribution on the conductor, and how the electric fields change. Explain what is going on. ii) Drag the conductor vertically upward, away from the dipole. Describe what is happening to the charge density on the conductor. Explain. iii) Suppose the dipole is an electrogenic fish, and the conducting object is its (conducting) prey. The electrogenic fish senses its prey by detecting changes in electric fields on its skin caused by the conducting prey. Move the prey around and watch the electric fields in the region of the dipole. Approximately how close must the conductor be to the dipole before it noticeably affects the electric field? What are your thoughts about this? There is no simple answer to this. It depends on several quantities, including the conductor size, and the point at which the electric field is being observed.4 B: Analog simulation Here you use a piece of carbonized paper in which currents flow to simulate electric fields and equipotential surfaces in vacuum. Field plotting board: Get a piece of graphite paper with two silver dots (representing conducting spheres), one on each end. On the field plotting board, first put down a sheet of printer paper, then a sheet of carbon paper, and finally the graphite paper on top. Power supply: Attach the +30V output of the DC power supply to one connector, and the ground output to the other (lab manual has a good description of all of this). This maintains a constant potential difference between the two painted conductors on the graphite sheet. Digital multimeter: Attach the red and black voltage probes to the Keithley digital multimeter (DMM) by attaching a BNC to banana-plug adaptor to each probe. Then connect a banana plug cable from the red terminal of red probe to the DMM red connnection, and from the red terminal of the black probe to the DMM black connection. Do not connect anything to the black terminal of either probe. Sit one probe in each of the field plotting board electrical connections. Turn the multimeter on. The multimeter can measure multiple quantities (voltage, resistance, or current), so you have to tell it to measure voltage by pushing the ‘V’ button. Put it on the 20V scale of the DC voltage measuring function by pushing the ‘20’ button. Adjustments: Turn on the DC power supply and adjust the voltage until the multimeter reads just less than 20V (the switch just above the connections should be on ‘30V’ and not ‘100V’). If the voltage is too high and the multimeter reads ‘OL’ (for ‘overload’), you should reduce the power supply voltage until you get a reading. Leave everything on and connected. The display on the multimeter is the electric potential difference across its inputs, ! Vred" Vblack. B1. Before starting the measurements, you determine the relation between voltage difference and electric field by doing a little calculation here while the power supply stabilizes. In the space below, use the relation between electric field and electric force on a charge to write down the electric potential difference between two points a small distance ! dr s = "x,"y( ) apart in terms of the x- and y-components of the


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UW-Madison PHYSICS 208 - EC-2: Electric Fields and Potentials

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