Lab-6_Magnetic Force_Field (1)

1102L-080/081; Lab 06 Rabbit year, Sum2, 2023 Lab 6: Magnetic Force on a Wire (100 points total) You will need to run a simulation to do the lab. Answer the following questions as you work through the lab . Write your answers in blue . (Note that we may miss your response if it does not stand out ) Submit the completed lab in PDF format in Canvas before the due date. Please do not email the lab to us. An email submission will NOT be accepted. Objectives: Calculate magnetic field from experimental data. 1. You will calculate the magnetic force from the force of gravity acting on a mass with current flowing through it. 2. You will find the relationship between magnetic force and length of the mass. 3. You will find the relationship between magnetic force and current passing through the mass. 4. You will extract information from the data collected and calculate magnetic field from a plot. Introduction: A current-carrying wire in a magnetic field experiences a force that is usually referred to as a magnetic force. The magnitude and direction of this force depend on four variables: the magnitude of the current ( I ); the length of the wire ( L ); the strength of the magnetic field ( B ); and the angle ( θ ) between the wire and the magnetic field. This magnetic force can be described mathematically by the vector cross product: ⃗ F B = I ⃗ L× ⃗ B , or in scalar terms F B = ILB sin θ (6.1) The vector ⃗ L is in the direction of the current I . In this part of the lab, we are going to investigate the dependence of the force on these variables. Read Ch 19: Sec 4, 7 for concepts. 1. A Magnetic Force Experiment: You will use the data collected in an experiment to measure magnetic field. The figure on the left shows the experimental setup. The figure below shows a schematic diagram of the experiment. Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 1

1102L-080/081; Lab 06 Rabbit year, Sum2, 2023 A rectangular wire loop is connected across a power supply with an emf of 20 V. The wire loop is then used in an experiment to measure the strength of the magnetic field between the poles of a magnet. The magnet is placed on a digital balance, and the wire loop is held fixed between the poles of the magnet, as shown. The 0.020 m long horizontal segment of the loop is midway between the poles and perpendicular to the direction of the magnetic field. The balance was adjusted to “ZERO” before turning ON the power supply. When the power supply in the loop is turned on, a 4.0 A current flows in the direction shown. 1A. The resistance of the wire according to Ohm’s Law is: __ 5 __  [3 points] 1B. The direction of the magnetic force on the wire segment in the magnetic field is Upwards / Downwards (use Right Hand Rule) [3 points] Various rectangular loops of wire with same total length (0.8 m) were constructed such that the lengths of the horizontal segments ( L ) of the wire loops varied between 0.02 m and 0.10 m. The horizontal segment of each loop was always centered bet ween the poles, and the current in each loop was always 4.0 A. The force reading of the balance changed every time the length of the wire was changed, and the power supply was turned on. The difference in reading is only due to the magnetic force on the wire. At equilibrium: ∑ ⃗ F = 0 → F down = F up; Here, F down = F B = ¿ Magnetic force and F up = ¿ Reading of the balance in Kg. There is no actual mass involved in this experiment. However, the magnetic force pushes down on the balance, just as a real mass would push down on the balance with its weight, F g . In terms of mass, we can write: F g = F B  ∆mg = ILB sin θ = ILB , ( θ = 90 °→ sin θ = 1 ) (6.2) where ∆m = m − m 0 , m 0 = ¿ mass reading without any current ( I = 0 ¿ Lab work (Remember to write your answer in a different font so that it stands out from the instructions) 2: Magnetic Force on a Rectangular Coil as a Function of the Length (L): Complete the table below [15 points] Current (A) Length of the wire (meter)  m (Kg) Magnetic Force, F b in (N) 0.02 0.006 0.0588 Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 2

1102L-080/081; Lab 06 Rabbit year, Sum2, 2023 B = 0.74725 Tesla 3: Magnetic Force on a Rectangular Coil as a Function of Current (I) [15 points] Length L (meter) Current I (A)  m (Kg) Force (N) 0.20 0.0 0.00 0 0.5 0.0077 0.074725 1.0 0.0153 0.14945 1.5 0.0230 0.224175 2.0 0.0306 0.2989 2.5 0.0383 0.373625 3.0 0.0460 0.44835 3.5 0.0536 0.523075 Plot Force as a function of Current. Make sure to label your axes with proper units to get full credit. [15 points] 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.1 0.2 0.3 0.4 0.5 0.6 f(x) = 0.15 x Force vs Current Current (A) Force (N) Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 4

1102L-080/081; Lab 06 Rabbit year, Sum2, 2023 3A. Find the slope of the line: Slope = ¿ 0.1495 (Remember to write proper units) [3 points] 3B. Compare the equation (6.1) with the equation of a straight line. What does the slope represent? Slope is representative of the proportional relationship of Force in Newton and Current (A) [3 points] 3C . Calculate the strength of the magnetic field (B) from the above information and Equation 6.1. Write the equation you used to figure out the value of B. . 7475 (.1495 N/A /.20m)= .7475 [3 points] B = 0.7475 Tesla 4. Conclusion Questions: 4A. A current-carrying wire is in a uniform magnetic field B. Under which circumstances does the force generated by the B field on the current-carrying wire become zero? [3 points] When the field and wire current are parallel, the force that the B field exerts on the wire that is carrying current is zero. 4B. Show that the unit of Magnetic Force (N) is equal to WbA/m. where Wb is Weber, A is Ampere and m is meter. We know that 1A = 1 C/s, and 1 Wb/m*1A= (1T*1m^2)/ m*1C/s. Therefore, 1 T = 1N/A*m. We then can correspond 1 Wb/m*1A = 1N/A*m * 1C/s or 1 N = 1 Wb A/m to understand how units cancel to show the relationship of Wb * A / m, [2 points] 4C. In what orientation should a current-carrying wire be located in a uniform magnetic field to experience a maximum force? Why? Since the force felt by the wire is a component of the cross product (u v), which has its maximum magnitude when u and v are perpendicular, the location of a current-carrying wire should be perpendicular or 90 degrees to be in a uniform magnetic field and to experience a maximum force. The greatest force would exist where the vectors u and v are the unit vectors in the direction of the magnetic field and current. [3 points] 4D. A wire carrying current in the –x axis is in an external magnetic field. What is the direction of the uniform magnetic field such that the magnetic force on the wire is maximized along –y axis? Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 5