LENZ'S LAW I. Induced currents ai ba EM 45 . A positive point charge is placed in the magnetic field of a solenoid as shown. Using if any . F = q3 X B, determine the direction of the magnetic force on the charge in each case below, . The charge is stationary. +q . The charge is moving to the right. . The charge is moving to the left. B. Suppose that the point charge is now replaced by a copper wire loop. 1. Determine the direction of the induced current in each case below, if any. Explain in terms of magnetic forces exerted on the charges in the wire of the loop. . The loop is stationary. . The loop is moving toward the solenoid. . The loop is moving away from the solenoid. e motion between the solenoid wad up meigs songs Nov 1 . woled sinshine ed) to ross diw songsaib 10 ssigs nov Joltedw sini? .d ode I pas aowens 159710? 2. For each case above in which there is an induced current, determine: insbure . the direction of the magnetic moment of the loop. (Hint: Find the direction of the magnetic field at the center of the loop due to the induced current in the loop. The magnetic moment is a vector that points in this same direction.) out of sub xult art to neig stieoggo arif earl ayowls gool orit of sub xult sif?" :S Inabuja . whether the loop is attracted toward or repelled from the solenoid. ed in the loop. This current ca ed hux through the loop that has osite sign to the change n the loop . whether the force exerted on the loop makes the loop speed up or slow down. Check your answers with a tutorial instructor before continuing. Tutorials in Introductory Physics, Physics Education Group, Department of Physics University of Washington (Summer 2022, Mazur version)EM Lenz's law 46 C. In each of the diagrams below, a loop is moving at constant speed in a magnetic field. The loop is moving to the right in case A and to the left in case B. In the table below, indicate the direction or sign of each of the listed quantities for both cases. (Recall that u indicates the magnetic moment of a current loop and @ indicates magnetic flux through a loop, defined as S B . dA.) Case B Case A Case A Bexternal Iinduced pol odd of gnivo Bind or 1P Case B 1 10 910 P external AP external P induced Compare your table with the members of your group. Resolve any inconsistencies. D. State whether you agree or disagree with each of the students below. If you agree, explain why. If you disagree, cite a specific case for which the student's statement does not give the correct answer. (Hint: Consider cases A and B above.) Student 1: "The magnetic field due to the loop always opposes the external magnetic field." Student 2: "The flux due to the loop always has the opposite sign as the flux due to the external magnetic field." Student 3: "The flux due to the loop always opposes the change in the flux due to the external magnetic field." Check your answers to parts C and D with a tutorial instructor before continuing Tutorials in Introductory Physics, Physics Education Group, Department of Physics University of Washington (Summer 2022, Mazur version)Lenz's law EM II. Lenz's law 47 A. The diagram at right shows a stationary copper wire loop in a uniform evem goof wilw A magnetic field. The magnitude of the field is decreasing with time. un on anw now 1. Would you predict that there would be a current through the loop: . if you were to use the idea that there is a magnetic force exerted reasoning on a charge moving in a magnetic field? Explain your . if you were to use the reasoning of the student in part D of section I with whom you agreed? Explain your reasoning. 2. It is observed that there is an induced current through the wire loop in this case. Use the appropriate reasoning above to find the direction of the current through the wire of the loop. To understand the interaction between the wire loops and solenoids in section I, we can use the idea that a force is exerted on a charged particle moving in a magnetic field. In each of those cases, there was an induced current when there was relative motion between the solenoid and the wire loop. In other situations such as the one above, however, there is an induced current in the wire loop even though there is no relative motion between the wire loop and the solenoid. There is a general rule called Lenz's law that we can use in all cases to predict the direction of the induced current B. Below is a statement of Lenz's law that is similar to what appears in many textbooks: If the net external flux through a wire loop changes, a current will be induced in the loop. This current creates an induced flux through the loop that has the opposite sign to the change in net external flux through the loop. Make sure you understand how Lenz's law is related to the statement by the student with whom you agreed in part D of section I. Tutorials in Introductory Physics, Physics Education Group, Department of Physics University of Washington (Summer 2022, Mazur version)EM Lenz's law 48 X- C. A wire loop moves from a X X XXXX region with no magnetic XXXX2 X X B field into a region with a XXXXB X X X x uniform magnetic field X ; :X X XXX VX - - X X U X X X pointing into the page. XXXXXX X X XXXX - W - The loop is shown at two W - instants in time, t = t and At time t + At At time t t = ti + At. 1. Is the magnetic flux through the loop due to the external field positive, negative, or zero: . at time ti? . at time ti + At? 2. Is the change in flux due to the external field during the interval At positive, negative, or zero? 3. Use Lenz's law to determine whether the flux due to the induced current in the loop is positive, negative, or zero. -gool 4. What is the direction of the current in the loop during this time interval? D. At two later instants, t = t2 XXXXX XXXX XXXXXXXXXX and t = t2 + At, the loop is XXXXXXX B X X XXXX XXXX located as shown. X X X X X X X X X = > X X ordi ban bionsloe sift nsewisd n om sitel At time t, At time to + At D. Suite whether you 1. Use Lenz's law to determine whether the flux due to the current induced in the loop is positive, negative, or zero. Explain your reasoning. 2. Describe the current in the loop during this time interval. Jesus baonbri 3. Consider the following student dialogue: will wal Student 1: "The sign of the flux is the same as it was in part C. So the current here will also be counter-clockwise." Student 2: "I agree. If I think about the force on a positive charge on the leading edge of the loop, it points towards the top of the page. That's consistent with a counter-clockwise current." Do you agree with either student? Explain your reasoning Tutorials in Introductory Physics, Physics Education Group, Department of Physics University of Washington (Summer 2022, Mazur version)