Lab-Magnetic+Fields

PHY 131 Fall 2023 Lab9-Fields in Wires-s20-Aviary.docx Experiment: The Magnetic Fields due to Electric Currents OBJECTIVES 1. Determine the relationship between magnetic field and distance in a current-carrying wire 2. Determine the relationship between magnetic field and current in a current-carrying wire 3. Use graphical analysis to determine the value of µ o Materials • Computer with internet access • The Physics Aviary simulation site • LoggerPro software Introduction When current flows through a long wire (i.e. length of wire >> di  stance from wire), a magnetic field ( B ) is generated due to the moving charge. Clearly the magnitude of the magnetic field depends on the size of the current ( I ) and the distance (r) away from the wire. In this experiment, you will explore two different but related physical la  ws to model the relationship between B , I and r: the Biot-Savart Law and Ampere’s Law . The Biot-Savart Law for magnetism is the equivalent of Coulomb’s Law for electric fields. Both physical laws describe a corresponding vector field quantity which is related to the ratio of the “source” of the field to the square of the distance from the source time a constant. One source of magnetic fields is the magnitude of current ( I ) that flows through a small element of wire ( ݈݀ ), or ݈݅݀ . The equation for the magnitude of a magnetic field due to this small “source” according to the Biot-Savart Law is ห݀ܤ ሬԦ ห = ߤ ௢ ݈݅݀ 4 ߨݎ ଶ sin ߠ where ߤ ௢ = 1.256 ݔ 10 ି଺ ்ή௠ ஺ , ߠ is the angle between the direction of the current element ( ݈݅݀ Ԧ ) and the distance vector is ݎԦ . Applying the Biot-Savart Law to calculate the magnitude of the magnetic field at a distance ( ݎ ) due to a straight current-carrying wire (with current i and length L) leads to the expression: หܤ ሬԦ ห = ߤ ௢ ݅ܮ 4 ߨݎ ට ܮ ଶ 4 + ݎ ଶ Alternatively, Ampere’s Law can be used to calculate the magnitude of the magnetic field vector due to a long straight current carrying wire, applicable when L>>r: หܤ ሬԦ ห = ߤ ௢ ݅ 2 ߨݎ Note: The direction of B  “curls” around the length of the wire according to the right-hand rule. Screenshot from ThePhysicsAviary.com

In this experiment, you will measure the magnetic field due to a straight wire at various distances from the wire (at constant current), as well as with various electrical currents (keeping the distance constant). You will model your data using Ampere’s Law. Lastly, you will use the model results to find an experimental value for the permeability constant in free space, µ o . Part A: Preliminary Observations 1. Open The Physics Aviary “Magnetic Field from a Wire” simulation: https://www.thephysicsaviary.com/Physics/Programs/Labs/FieldFromWire/ 2. Get familiar with the controls . a. Click on “Field Strength” button to observe the magnitude of the magnetic field. Describe the shape of the field lines near the wire. Sketch some the field lines around the wire.. b. Click on “Location of the Field Sensor”. Use the arrows to move the field sensor up and down. How does the field strength vary with vertical position? How does the field strength vary with horizontal position? c. Click on “Current” to observe the magnitude of the electric current in the wire. Use the arrows to vary the current up and down. What direction are the electrons moving in the wire and what does this indicate about the direction of the current? How does the field strength vary with current strength? d. Click on “Direction” to switch the direction of the current in the wire. How does the field change when you switch current direction?