Activity 5 Potential and Resistivity Purpose This activity takes you through the process of computing the electric field of a system of conductors and dielectrics and of reasoning about the work required to move a charged particle in an electric field. 5.1 Warm Up Questions Answer the following two questions individually without consulting your lab partners. Activity Problem 5.1 A positive point charge is placed in a cavity inside a neutral conductor without transferring charge to the conductor, as shown in the figure to the right. What is the sign of the charge on the surface of the cavity and the outer surface of the conductor? conductor +Q Select One of the Following: (a) There is no charge on the surface of the cavity or the outer surface of the conductor. (b) There is a positive charge on the surface of the cavity, but no charge on the outer surface of the conductor. (c) There is a negative charge on the surface of the cavity, but no charge on the outer surface of the conductor. (d) There is no charge on the surface of the cavity, but a positive charge on the outer surface of the conductor. (e) There is a negative charge on the surface of the cavity, and a positive charge on the outer surface of the conductor. Activity Problem 5.2 A positive point charge with charge +Q is placed and held inside a cavity in a neutral conductor as drawn. No charge is transferred to the conductor as the point charge is placed. The conductor is then grounded. Is there a non-zero electric field outside the conductor after grounding? If there is, what is the direction of the electric field outside of the conductor after grounding? conductor 1 +Q Select One of the Following: (a) The electric field outside the conductor is zero. (b) The electric field points generally away from the conductor. (c) The electric field points generally toward the conductor. Now work with your lab partners to come to a consensus about the answer. If you cannot, call your TA in for some help. Once the group has reached one answer, record the answer and a good explanation (preferrably with pictures) to each question below. Analysis-5.1:Answer and Explanation to Question 5.1 Analysis-5.2:Answer and Explanation to Question 5.2 5.2 Reasoning About the Sign of Work In this activity, we are going to reason about the amount of work it takes to push an electric charge through an electric field and get to play with an extremely addictive field drawing program. 5.2.1 The System For this section, we will work on the system of charge drawn below. Don’t draw the field map quite yet. 2 +1 B 3 -2 -2 2 1 A 5.2.2 Reason About the Field Predict-5.3:Five points, A, 1, 2, 3, and B are labelled on the figure. Approximately draw the electric field vector at each point to scale. 5.2.3 Test your reasoning Start to the computer program we used in Lab 3 which can be to accessed in the Lab Manual Folder in eCampus. First, use the program to test your reasoning about the electric field. • Click on the “+” icon at the left to bring up the menu of point charges. • Add point charges to construct the configuration above, placing each charge at a grid point. • Leave space for the points A, 1, 2, 3, B also to be grid points. • Now select the “Field” icon with the arrow symbol from the left menu. 3 • Click on each of the points A, 1, 2, 3, B to have the computer draw the actual field vectors. Computer-5.4:In a different color, add the field vectors the computer drew to the diagram. Compare with Prediction-5.5:How do your field vectors compare to the computer’s? If your vectors were very different, what assumption were you making that was incorrect? 5.2.4 Draw an Electric Field Map Draw-5.6:Draw the electric field map using 4 lines per Q. 5.2.5 Check Your Electric Field Map Use the electric field mapping program to draw the field map by selecting “Field” icon with the line symbol from the left menu. Analysis-5.7:If the general shape of the two maps was not the same, what went wrong? 5.2.6 Recall Work In Physics 111 (I hope), you learned that work was force times distance, or more precisely the work done by an external agent is W = F⃗applied · ∆⃗x. The agent does positive work on an object if the agent has to push on the object in the direction the object is moving. An agent does negative work on an object if the agent pulls in the opposite direction the object is moving. We are going to imagine moving a +1C (yes, that is a large charge) very slowly, such that its kinetic energy is approximately zero, along the line from A to B. In the table below, record whether you as the external agent would have to push or be pulled by the +1C in each of the segments along the dashed line. If you push, then the work you do is positive. If you are pulled, then the work you do is negative. Record whether you do positive or negative work to move the charge. Remember, only the force along the direction of motion matters. 5.2.7 Use the Program to Compute the Work Select the potential difference icon from the menu at the left; it is labeled ∆V , pronounced “delta V.” Potential difference is work done by an external agent (in this case you) per unit charge. Use the program to compute the work (potential difference times 1C) required to move the 1C charge between each adjacent pair of points along the dashed line. You do this by clicking on the first point and dragging toward the second point. The program will report the potential difference to the right of the grid as you drag. Since work, W , is the potential difference multiplied by the charge moved, if the kinetic energy does not change, then W = Q∆V . If you recorded a potential difference of 0.15V (V is a volt), then the work is W = Q∆V = (1C)(0.15V) = 0.15J where J is a joule. Record the values for work in the table that follows. Measure-5.8: Segment Push or Pull A⇒1 1⇒2 2⇒3 3⇒B Work is Positive or Negative Work = 1C× Potential difference 4 Analysis-5.9:Do the values you measured, using the program, agree with the sign you reported for the work? YES or NO If no, discuss the difference with the instructor. 5.3 Potential Energy If we are continuing to recall Physics 111, then you will recall that if the kinetic energy does not change then the work was related to potential energy. Work Done by External Agent = Change in Potential Energy of the System As a charged particle is moved from point A to point B the potential energy of the particle will change. 5.3.1 Sketch the Potential Energy As the external agent does work, pushes the particle, the potential energy of the system increases. As the external agent restrains the particle (pulls), the potential energy of the particle decreases. Recall also, that the point where the potential energy was zero was arbitrary. When you worked with gravitational potential energy, one usually arbitrarily defined the floor as having zero potential energy. Predict-5.10:On the figure to the right sketch the potential energy of a positive charge placed in your field map as it is moved from point A to point B along the line in the figure. Let the system have zero potential energy at point A . 5.3.2 Potential Energy A 1 2 3 B Check Your Reasoning If we assume we are moving a 1C charge, the field mapping program will calculate the potential energy for you. The potential energy at point P is the potential difference between the point A and the point P multiplied by 1C if we assume the potential energy is zero at point A. You have already used the potential difference tool in the previous section. Observe-5.11:Measure the potential difference between A and each of the points 1, 2, 3, and B. Point 1 2 3 B Measure Between A⇒1 A⇒2 A⇒3 A⇒B Potential Energy = 1C× Potential difference 5 Draw-5.12:Use your measurement above to plot the potential energy at the points A, 1, 2, 3, and B to the right. Potential Energy Compare with Prediction-5.13:How do the two plots compare? If the two plots are very different, what assumptions were you making that were in error? A 5.3.3 1 2 3 B Potential Energy and Motion A particle, if free to move, will always move to lower its potential energy. It will slide down the potential energy curve. Analysis-5.14:If a particle is placed in your potential energy curve at point B, which direction does it move to lower its potential energy? (toward A or away from A). Is this consistent with the force you found at point B in the previous section? 5.4 5.4.1 Resistivity of Materials Electric Current And Resistance We are going to get a little ahead of ourselves at this point, but the additional concept we need, electric current, is already familiar to many of you. For a conductor in a static situation where the electric charge densities are constant, the electric potential across a conductor is zero. If the charge densities are not constant, then charge is moving around (Conservation of Charge). We will call the motion of electric charge an electric current and use the symbol I to denote it. The electric current is just the charge per unit time flowing through some surface. Q ∆t I= (5.1) The electric potential difference across a perfect conductor is zero, but, alas, real conductors are not perfect, so when you pass a current through a conductor a potential difference, ∆V , develops across the conductor. For different conductors, you will get difference voltages for the same current. We will define the resistance of the conductor as the ratio of voltage across the conductor to the current through it. R= 5.4.2 ∆V I (5.2) Resistivity Because different materials consist of different atoms with different bonding, they react differently to electric current. This reaction to current is called resistivity, denoted by ρ, and it relates to how much the material resists the flow of electrons. Since resistivity is a function of the type of atoms in a material, each material has a unique resistivity. In this lab, we will use this property as a way of identifying different unknown materials The total resistance, R, of any material to current depends not only on the nature of the atoms of the material (resistivity, ρ) but also on the length, L, and the cross-sectional area, A, of the material as seen in Eq. 5.3. 6 ρL (5.3) A Note, we have now reached the unfortunate part of the course where we start to re-use symbols. The resistivity has nothing to do with volume charge densities which use the same symbols. R= 5.4.3 Preliminaries There are several threaded rods with wire of unknown materials wound around them or spools of wire in the lab. To determine the materials from which these samples of wire are made, you will measure the voltage across and current through each wire, use this to calculate the resistances, and then use the dimensions of the wire to calculate the resistivity. Table 5.1 contains the American Wire Gauge (AWG), the gauge of each wire, in each of the 5 coils. This is a measure of the diameter of the wire. Table 5.2 contains common wire gauges which I found on Wikipedia. For reference, your house is probably wired with 12 AWG. Calculate-5.15:Record the diameter of each wire in millimeters in Table 5.1 and then calculate the cross-sectional area, A, of each wire in meters2 . The cross-sectional area is the area of the circle with the diameter of the wire. Be care to convert millimeters to meters and to use the area of a circle in terms of the diameter. Table 5.1 - Wire Dimensions AWG Material 1 16 Material 2 24 Material 3 16 Material 4 16 Material 5 18 Diameter (d) meters Area (A) meters2 Table 5.2 - American Wire Gauge AWG 12 14 16 18 20 22 24 Diameter (d) millimeters 2.053 1.628 1.291 1.024 0.812 0.644 0.511 7 5.4.4 Method 1: Using Definition of Resistance Prepare this the spool of wire for voltage and current measurements by connecting the circuit shown at the right. There are two meters, digital multimeters (DMM), in the circuit. One should be set to measure current and the other voltage. Your TA will describe how to set the meters properly. The table below will be used to record the measurements for this section of the lab. The length of each wire, L, has been provided. Copy the area of the wire from the previous section to the table. Power Supply DMM Amps COM V-A Coil DMM Volts COM V-A • Adjust the power supply so it delivers no more than 0.1A. • Record the voltage and current in Table 5.3 for each material. • Calculate the resistance, R = ∆V /I, for each spool or coil and record it in in Table 5.3. • Using the measured values of R, the provided L, and your calculatedA, calculate the resistivity, ρ. Disconnect the unknown wire from the circuit. Table 5.3 - Resistivity L (m ) Material 1 3 Material 2 1 Material 3 1 Material 4 2 Material 5 100 5.4.5 A (m2 ) Voltage ( ) Current ( ) Resistance ( ) Resistivity ( ) Identity the Material The table below list the resistivities for a number of common metals. Table 5.4 - Resistivity of Common Metals Resistivity, ρ Material (ohm-m) Resistivity, ρ Material Silver 1.59 × 10−8 Brass Copper 1.68 × 10−8 Carbon Steel Aluminum 2.65 × 10−8 Stainless Steel Tungsten 5.6 × 10−8 Zinc Nickel 6 × 10−8 6.3 × 10−8 Platinum (ohm-m) 7 × 10−8 Material (ohm-m) Constantan 4.9 × 10−7 1.0 × 10−7 Monel 5.1 × 10−7 1.0 × 10−7 Titanium 1.06 × 10−7 Mercury 9.8 × 10−7 2.2 × 10−7 Nichrome 1.00 × 10−6 Lead Manganin Resistivity, ρ 4.82 × 10−7 8 Quartz (Fused) 8 × 10−7 7.5 × 1017 Analysis-5.16:Using the resistivity values in Table 5.4, identify the material with the closest resistivity and record the result in Table 5.5. Table 5.5 - Identity of Unknown Materials Identified Material Material 1 Material 2 Material 3 Material 4 Material 5 5.5 Group Problems Work the following problems as a group, but each member of the group should write his or her own solution. Activity Problem 5.3 The figure to the right shows a region of space containing an electric field. The field is such that the system has the equipotential surfaces drawn. The electric potential of each surface is labeled. The electric potential changes smoothly between the surfaces drawn. If a positive particle is released from rest at point P , which of the following best describes its motion? 10V P 20V 30V Select One of the Following: (a) The particle stays at rest at point P . (b) The particle moves towards the top of the page with constant speed. (c) The particle moves towards the top of the page with decreasing speed. (d) The particle moves towards the top of the page with increasing speed. (e) The particle moves towards the bottom of the page at a constant speed. (f) The particle moves towards the bottom of the page with decreasing speed. (g) The particle moves towards the bottom of the page with increasing speed. 9 Activity Problem 5.4 The figure to the right shows four equipotentials labelled 1, 2, 3, and 4. Select the inequality below that is obeyed by the electric potentials of these equipotential surfaces. 2 Select One of the Following: 3 (a) V1 > V2 > V3 > V4 (b) V1 < V2 < V3 < V4 1 (c) V2 = V3 > V1 = V4 4 (d) V2 = V3 < V1 = V4 (e) V3 > V1 = V2 > V4 5.6 Summary Summary-5.17:In your own words using about three sentences, summarize the most important things you discovered in this lab. Signature:To Be Completed 10 Finished 
Purchase answer to see full attachment