Magnetic_Fields_and_Forces_VLab_2023 (1)

Virtual Lab: Magnetic Fields and Forces Name(s) : Date: Introduction Analogous to how electric charges produce electric fields, all moving electric charges produce magnetic fields. Similarly, just as electric charges exert electric forces on each other, the magnetic fields of moving charges exert magnetic forces on each other. An electric current flowing through a wire is a collection of moving charges and therefore has a magnetic field. This magnetic field forms closed loops around the wire, and its strength decreases with distance from the wire. The magnetic nature of current-carrying wires was discovered in 1819 by the Danish scientist Hans Christian Oersted. This demonstrated the connection between electricity and magnetism and paved the way for the modern era of electric motors and generators. The connection between electricity and magnetism can be demonstrated in the laboratory. If a magnetic compass is brought near a current-carrying wire, it is deflected due to the magnetic field of the wire. In the same way, if a current-carrying wire is placed in the magnetic field of a magnet, it will feel a force due to the interaction of its own magnetic field, and that of the external magnet. Current-carrying wires exert magnetic forces on each other. This property was first investigated by the French scientist Andre-Marie Ampere. He found that two parallel wires carrying an electric current in the same direction exert an attractive force on each other. On the other hand, if the currents in these two parallel wires flow in opposite directions, then they repel each other. The magnitude of this force (F) is given by: F = ILB sin α [ 1 ] where I is the strength of the current flowing through the wire (in amperes), L is the length of wire in the magnetic field, B is the strength of the magnetic field, and α is the angle between the wire and the magnetic field. Based on Newton’s third law, the two wires exert forces of equal magnitude, but opposite direction on each other. The strength of the magnetic field ( B ) at a distance r from a long, straight wire carrying a current I , is given by: B = μ 0 I 2 πr [ 2 ] 1

where  0 is the permeability constant: μ 0 = 1.26 × 10 − 6 T m / A From equation [2], we see that the magnetic field strength ( B ) around a current-carrying wire decreases with distance in an inverse relationship ( 1/r ). In part A of this lab, we will investigate the magnetic field around a current-carrying wire and verify equation [2]. In parts B and C of the lab, we will explore forces acting on current-carrying wires. Part A Magnetic field of a current-carrying wire In this part of the lab, we will study how the strength of the magnetic field of a current- carrying wire changes with distance. We will use a free online simulation provided by Prof. Frank McCulley at “The Physics Aviary.” You can access this simulation at this website: https://www.thephysicsaviary.com/Physics/Programs/Labs/FieldFromWire/index.html Read the instructions on the simulation start page and then click on “ Begin .” The animation uses a magnetic field sensor to measure the strength of the magnetic field ( B ) at different distances from a current-carrying wire. 1. Click on the “ Grid ” tab and move the “ Magnetic field sensor ” to a distance of 1 cm from the wire using the “ Location of Field Sensor ” arrows as shown in the figure below. Click on the “ Field Strength ” and “ Current ” tabs to display their values. Change the direction of current to conventional (right to left). Use the current value closest to 2.5 A . Click on “ Field Strength ” at the top right and record your measured magnetic field in tesla (T) in Table 1 below. Record the absolute value (ignore any negative signs). Click on “ Field ” at the top to view the closed loops of the magnetic field encircling the wire. Record the direction of the magnetic field at the top of the wire where the sensor is located. The first row has been completed as an example. You may replace this row with your own measurements. Enter the magnetic field values using “ e ” for the exponent instead of “x10^” for easier graphing in Excel. Note : one microtesla (1 μT) is 1e -6 Tor 10 -6 T. 2. Move the magnetic field sensor to a distance of 2 cm from the wire and record the magnetic field strength in row 2. Keep the current fixed at the same value (about 2.5 A). 2

Table 1 Current strength (amperes) Distance from wire (meters) Magnetic field magnitude (tesla). Take the absolute value, ignore the negative sign. Magnetic field direction at location of sensor (using the right-hand rule) 2.6 0.01 51.43e-6 Into the screen Make a graph of Magnetic field strength ( tesla ) on the y -axis, versus Distance ( meters ) on the x -axis. Make sure your magnetic field values have the correct exponents, and you use the absolute values of the magnetic fields. Choose the chart type “Scatter with smooth lines and markers.” Click on the green “+” sign at the top right of the graph (for “Chart Elements,” and add a graph title and axes labels. In the “Chart Elements” menu, select “Trendline,” select the “Power” function option for the trendline, and select “Display equation on chart.” Answer questions A1 and A2 at the end of this document. Copy and paste your graph below: Copy-paste your graph from Excel here: 4

Part B Magnetic force on a current-carrying wire In this part of the lab, we will explore the forces exerted by magnetic fields created by charges moving inside a wire. 1. We will first work with an animation provided by The Magnet Academy. You can open the animation called “Lorentz Force” by Ctrl+clicking on, or copy-pasting the link below into your browser: https://nationalmaglab.org/magnet-academy/watch-play/interactive-tutorials/lorentz- force/ After it finishes loading, your animation window should look like the picture below. The arrow showing the direction of the current has been added to help you. The green wire carries current from the positive terminal of the battery to its negative terminal. The orange portion of the wire is placed between the magnetic field of a horseshoe-shaped magnet. If you click on the “Knife Switch” the circuit is closed, allowing current to flow. The current-carrying wire will produce its own magnetic field. The magnetic field created by the orange part of the wire will interact with the field of the horseshoe magnet and thereby experience a force. The direction of this force is given by the right-hand rule: point the fingers of your right hand in the direction of the current , 5

Series Connection Parallel Connection Figure 2 : Explanation of the forces on wires animation. The two wires shown in red are arranged in “ Series ,” therefore the current flows in opposite directions inside them. The current in the wire on the left flows “ down ,” and the current in the wire on the right flows “ up .” 2. Click on “ Run ” to observe the interaction between the wires. Do the forces between them cause them to attract (move closer) or repel (move away from each other)? Record your answer after step 6 below. 3. Observe the blue loops showing the magnetic fields around each wire, and the blue arrows showing the direction of these fields. For the central region between the two red wires, observe whether the fields from the two wires are in the same direction, or in opposite directions. Note : you can click on “ Pause ” to see the directions of the blue arrows better. Record your answer below. 7

4. Change the arrangement of the wires to “ Parallel ” by clicking on the “Parallel Circuit” button. 5. Click on “ Run ” and observe whether the forces between them cause them to attract (move closer) or repel (move away from each other). Record your answer below. 6. Observe the blue loops showing the magnetic fields around each wire and the blue arrows showing the direction of these fields. For the central region between the two red wires, observe whether the fields from the two wires are in the same direction, or in opposite directions. Note : you can click on “ Pause ” to see the directions of the blue arrows better. Record your answer below, and also answer questions C5 to C8 at the end of this document. Q1. For, two wires in series (currents in opposite direction), the forces cause the two wires to ______. Answer: Q2. For wires in series (current in opposite direction), the directions of the magnetic fields between the two wires are ______. Answer: Q3. For two wires in parallel (current in the same direction), the forces cause the two wires to ______. Answer: Q4. For wires in parallel (current in the same direction), the directions of the magnetic fields between the two wires are ______. Answer: 8

c) both the wires move downwards towards the floor d) both the wires move upwards towards the ceiling C6 . In part C of the lab, when two wires are in series , so that current flows in opposite directions inside them, the directions of the magnetic fields in the region between the two wires are ______. a) the same, and in the vertical direction (they both point upwards towards the ceiling) b) opposite vertically (one points up, while the other points down) c) the same, and in the horizontal direction (they both point towards the knife switch) d) opposite horizontally (one points towards the knife switch, the other points towards the battery) C7 . In part C of the lab, when two wires are in parallel , so that the current flows in the same direction inside them, we see that the wires move ____. a) towards each other (they attract) b) away from each other (they repel) c) both the wires move downwards towards the floor d) both the wires move upwards towards the ceiling C8 . In part C of the lab, when two wires are in parallel , so that the current flows in the same direction inside them, the directions of the magnetic fields in the region between the two wires are ______. a) the same, and in the vertical direction (they both point upwards towards the ceiling) b) opposite vertically (one points up, while the other points down) c) the same, and in the horizontal direction (they both point towards the knife switch) d) opposite horizontally (one points towards the knife switch, the other points towards the battery) After you finish, please save this document, and enter your answers in the accompanying lab quiz on eCampus for a grade. You do not need to submit a completed lab report for this lab. Thank you. 10