Physics 132: Lecture 15 Elements of Physics II Agenda for Today Lenz Law Emf opposes change in flux Faraday s Law Induced EMF in a conducting loop Physics 132: Lecture 15, Pg 1
Lenz s Law Physics 132: Lecture 15, Pg 2
Student questions why can a wire cause an induced current in another wire without moving? Can you clarify the significance of 'immediately after' closing a switch and 'long after' closing a switch? Thanks. I don't get physics I still dont really understand the concept of finding the direction of current in a loop if the B field is increasing or decreasing. It would be great if you just went over that concept again! What happens at the electron level that causes magnetism? Specifically, how does an electron's spin cause magnetism and why are some elements innately magnetic while others are essentially not? Physics 132: Lecture 15, Pg 3
Clicker Question 0: A conducting rod slides on a conducting track in a constant B field directed into the page. What is the direction of the induced current? a) clockwise b) counterclockwise c) no induced current x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x v Physics 132: Lecture 15, Pg 4
Lenz s Law Why? Does lenz's law apply to the moment of the change in flux or will the induced B field be the "permanent" field after the change. Physics 132: Lecture 15, Pg 5
Reasoning Strategy Lenz s Law 1. Find the direction of the magnetic flux that penetrates the coil. 2. Determine whether the magnetic flux that penetrates the coil is increasing or decreasing. Increasing: induced b-field opposes magnetic flux Decreasing: induced b-field aligned with magnetic flux 3. Use Curly RHR- to determine the direction of the induced current. Student: So is it more precise to say that there will be induced current if there s a change in magnetic flux/change in B field inside the enclosed area of the loop rather than just the entire B field? Student: There is one thing I'm wondering about Lenz's law. Magnetic flux is a scalar value, and so when we say that the induced field must counteract the change in magnetic flux, the only way to see whether this means the induced field must point up or down is to see which was the original field pointed, right? Physics 132: Lecture 15, Pg 6
Clicker Question 1: The bar magnet is pushed toward the center of a wire loop. Which is true? A. There is a clockwise induced current in the loop. B. There is a counterclockwise induced current in the loop. C. There is no induced current in the loop. Physics 132: Lecture 15, Pg 7
Correct: The loop creates an induced magnetic field opposite of the actual magnetic field to keep the magnetic flux constant. Since the induced field points into the page, the current will flow clockwise because of the right hand rule. The change in flux is increasing out of the page, so by the righthand rule a clock-wise current is needed to induce a magnetic field pointing into the page. When the magnetic field is increasing the induced field of the induced current is pointing in the opposite direction of the magnetic field. I used the curly right hand rule : thumb points in direction of induced magnetic field and fingers curl in direction of induced current. Science Clicker Question 1: Incorrect: The external magnetic field points out, the induced field must always counteract this field and point in. Physics 132: Lecture 15, Pg 8
The two loops of wire in the figure are stacked one above the other. Does the upper loop have a clockwise current (from above), a counterclockwise current, or no current at the following times? Before the switch is closed. (a) The current will flow counterclockwise. (b) The current will flow clockwise. (c) There will be no current. Clicker Question 2: Physics 132: Lecture 15, Pg 9
The two loops of wire in the figure are stacked one above the other. Does the upper loop have a clockwise current (from above), a counterclockwise current, or no current at the following times? Immediately after the switch is closed. (a) The current will flow counterclockwise. (b) The current will flow clockwise. (c) There will be no current. Clicker Question 3: Physics 132: Lecture 15, Pg 10
The two loops of wire in the figure are stacked one above the other. Does the upper loop have a clockwise current (from above), a counterclockwise current, or no current at the following times? Long after the switch is closed. (a) The current will flow counterclockwise. (b) The current will flow clockwise. (c) There will be no current. Clicker Question 4: Physics 132: Lecture 15, Pg 11
The two loops of wire in the figure are stacked one above the other. Does the upper loop have a clockwise current (from above), a counterclockwise current, or no current at the following times? Immediately after the switch is reopened. (a) The current will flow counterclockwise. (b) The current will flow clockwise. (c) There will be no current. Clicker Question 5: Physics 132: Lecture 15, Pg 12
Demo Induced current in coils Physics 132: Lecture 15, Pg 13
Clicker Question 6: A circular conducting loop is being moved upward (toward a current-carrying wire) at a constant speed. What will be the direction of the induced current? (a) (b) (c) No current will be induced (no flux change). Current will be induced clockwise. Current will be induced counter-clockwise. Physics 132: Lecture 15, Pg 14
Test 2 Coverage and Review Test 2: Tuesday, March 14 Will cover material from lectures 7 13 Xing Office hours This week: MW 2-3, R 2-4 MP 121B Review Sessions: F 3-5 pm in room MP 125A Mon the 13 th from 1-2 pm in room MP 129F Make appt. or just stop by Meyertholen Office hours (this week) T 1-3pm MP 129A, R 10-12pm MP 129A F 1-3pm MP 125B TA office hours Drop in centre (MP 125): check schedule online Physics 132: Lecture 15, Pg 15
Faraday s Law An emf is induced in a conducting loop if the magnetic flux through the loop changes. The magnitude of the emf is: The direction of the emf is such as to drive an induced current in the direction given by Lenz s law. Physics 132: Lecture 15, Pg 16
Using Faraday s Law If we slide a conducting wire along a U-shaped conducting rail, we can complete a circuit and drive an electric current. We can find the induced emf and current by using Faraday s law and Ohm s law: Physics 132: Lecture 15, Pg 17
A 4 cm 3 cm rectangular loop is made of a wire with resistance of 3.5 Ohm. The loop is placed in a region of uniform magnetic field, B = 5 T. The direction of B is perpendicular to the plane of the loop and points into the page as shown. The magnetic field starts to increase at a uniform rate of 0.1 T/sec. What is the magnitude of the induced current in the loop? (a) (b) (c) (d) (e) I = 0 A I = 3.4 10-5 A I = 1.2 10-4 A I = 0.02 A I = 4.8 A Example: Physics 132: Lecture 15, Pg 18
Example: A 4 cm 3 cm rectangular loop is made of a wire with resistance of 3.5 Ohm. The loop is placed in a region of uniform magnetic field, B = 5 T. The direction of B is perpendicular to the plane of the loop and points into the page as shown. The magnetic field starts to increase at a uniform rate of 0.1 T/sec. What is the magnitude of the induced current in the loop? Physics 132: Lecture 15, Pg 19
Clicker Question 8: A 4 cm 3 cm rectangular loop is made of a wire with resistance of 25 Ohm/m. The loop is placed in a region of uniform magnetic field, B = 5 T. The direction of B is perpendicular to the plane of the loop and points into the page as shown. The magnetic field starts to increase at a uniform rate of 0.1 T/sec. What is the direction of the induced current? (a) (b) (c) counterclockwise clockwise There is no induced current. Physics 132: Lecture 15, Pg 20
A solenoid with cross sectional area A = 4 10-4 m 2 is 0.120 m long and has 2500 turns. The magnetic field at the center of the solenoid is 5 10-3 T pointing into the page. A square wire loop 1.5 cm on each side is fixed inside the solenoid as shown. The current in the solenoid is uniformly decreased to zero over 10 seconds. What is the magnitude of the induced emf in the square loop? (a) (b) (c) (d) (e) 1.125 10-7 V 1.259 10-7 V 2.124 10-7 V 2.486 10-6 V 1.124 10-6 V Direction? CW Example: Physics 132: Lecture 15, Pg 21
Example: A solenoid with cross sectional area A = 4 10-4 m 2 is 0.120 m long and has 2500 turns. The magnetic field at the center of the solenoid is 5 10-3 T pointing into the page. A square wire loop 1.5 cm on each side is fixed inside the solenoid as shown. The current in the solenoid is uniformly decreased to zero over 10 seconds. What is the magnitude of the induced emf in the square loop? Physics 132: Lecture 15, Pg 22
Applications of Faraday s Law Electric Guitar A vibrating string induces an emf in a coil A permanent magnet inside the coil magnetizes a portion of the string nearest the coil As the string vibrates at some frequency, its magnetized segment produces a changing flux through the pickup coil The changing flux produces an induced emf that is fed to an amplifier Physics 132: Lecture 15, Pg 23
Applications of Faraday s Law Microphone Physics 132: Lecture 15, Pg 24
Applications of Faraday s Law Apnea Monitor The coil of wire attached to the chest carries an alternating current An induced emf produced by the varying field passes through a pick up coil When breathing stops, the pattern of induced voltages stabilizes and external monitors sound an alert Physics 132: Lecture 15, Pg 25
Eddy Currents Consider pulling a sheet of metal through a magnetic field. Two whirlpools of current begin to circulate in the solid metal, called eddy currents. The magnetic force on the eddy currents is a retarding force. This is a form of magnetic braking. Physics 132: Lecture 15, Pg 26
Application - Induction stove Physics 132: Lecture 15, Pg 27
Induced Fields Physics 132: Lecture 15, Pg 28
Maxwell s Theory of Electromagnetic Waves A changing electric field creates a magnetic field, which then changes in just the right way to recreate the electric field, which then changes in just the right way to again recreate the magnetic field, and so on. This is an electromagnetic wave. Physics 132: Lecture 15, Pg 29