Induced EMF Physics 132: Lecture e 21 Elements of Physics II Agenda for Today Force on moving charges Induced Current Magnetic Flux Area Vector Physics 201: Lecture 1, Pg 1
Clicker Question 11: A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides ab and cd. The loop will: (a) move to the right (b) move to the left (c) move up (d) move down (e) rotate d c B a b Physics 201: Lecture 1, Pg 2
Atomic Magnets A plausible explanation for the magnetic properties of materials is the orbital motion of the atomic electrons. The figure shows a simple, classical model of an atom in which a negative electron orbits a positive nucleus. In this picture of the atom, the electron s motion is that of a current loop! An orbiting electron acts as a tiny magnetic dipole, with a north pole and a south pole. Physics 201: Lecture 1, Pg 3
Magnetic Effects of Electrons Spins Electrons also have spin The classical model is to consider the electrons to spin like tops It is actually a quantum effect Physics 201: Lecture 1, Pg 4
Magnetic Properties of Matter For most elements, the magnetic moments of the atoms are randomly arranged when the atoms join together to form a solid. As the figure shows, this random arrangement produces a solid whose net magnetic moment is very close to zero. Physics 201: Lecture 1, Pg 5
In iron, and a few other substances, the atomic magnetic moments tend to all lineupinthesame direction, as shown in the figure. Materials that behave in this fashion are called ferromagnetic, with the prefix ferro meaning iron-like like. Ferromagnetism Physics 201: Lecture 1, Pg 6
Ferromagnetism A typical piece of iron is divided into small regions, typically less than 100 m in size, called magnetic domains. The magnetic moments of all the iron atoms within each domain are perfectly aligned, so each individual domain is a strong magnet. However, the various magnetic domains that form a larger solid are randomly arranged. Physics 201: Lecture 1, Pg 7
Physics 201: Lecture 1, Pg 8
Induced Magnetic Dipole If a ferromagnetic substance is subjected to an external magnetic field, the external field exerts a torque on the magnetic dipole of each domain. The torque causes many of the domains to rotate and become aligned with the external field. Physics 201: Lecture 1, Pg 9
Flat RHR Review RHR Direction of force + charge/current moving in B field? Out of page Curly RHR #1 Direction of B-field from loop of wire? Out of page + + + + Curly RHR #2 Direction of B-field from wire? CCW v Physics 201: Lecture 1, Pg 10
So far Moving charges create B-fields (cause magnets) Atomic level: electrons cause magnetism Current in a wire B-fields exert forces on moving charges Current carrying wire feels a force Now: change in B-field causes moving charges!!! Physics 201: Lecture 1, Pg 11
Faraday s Law Key to EVERYTHING in E+M Generating electricity Microphones, o Speakers e and Tape Decks Amplifiers Electric Guitars Changing B-field creates E-field Physics 201: Lecture 1, Pg 12
Faraday s Discovery of 1831 When a bar magnet is pushed into a coil of wire, it causes a momentary deflection of the current-meter needle. A quick withdrawal of the magnet deflects the needle in the other direction. Holding the magnet inside the coil has no effect. Physics 201: Lecture 1, Pg 13
Motional EMF Physics 201: Lecture 1, Pg 14
Motional EMF Physics 201: Lecture 1, Pg 15
Motional EMF Physics 201: Lecture 1, Pg 16
Motional EMF The magnetic force on the charge carriers in a moving conductor creates an electric field of strength E = vb inside the conductor. For a conductor of length l, the motional emf perpendicular to the magnetic field is: Physics 201: Lecture 1, Pg 17
Clicker Question 1: A metal bar moves through a magnetic field. The induced charges on the bar are Physics 201: Lecture 1, Pg 18
Induced Current If we slide a conducting wire along a U-shaped conducting rail, we can complete a circuit and drive an electric current. If the total resistance of the circuit is R, the induced current is given by Ohm s law as: Physics 201: Lecture 1, Pg 19
Induced Current The figure shows a conducting wire sliding to the left. In this case, a pushing force is needed to keep the wire moving at constant speed. Once again, this input power is dissipated in the electric circuit. A device that converts mechanical energy to electric energy is called a generator. Physics 201: Lecture 1, Pg 20
Clicker Question 2: A metal ea bar of length 1.5 m is spulled edao along ga track at a velocity of 4 m/s. A magnetic field of 2 T points into the page. What current flows through the 2 resistor? (a) 12 Amps (b) 6 Amps (c) 2 Amps (d) 24 Amps (e) 3 Amps Physics 201: Lecture 1, Pg 21
Clicker Question 3: A metal ea bar of length 1.5 m is spulled edao along ga track at a velocity of 4 m/s. A magnetic field of 2 T points into the page. What direction does the current flow through the resistor? (a) Top to bottom (b) Bottom to top Physics 201: Lecture 1, Pg 22
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 201: Lecture 1, Pg 23
Magnetic Flux Number of B-field lines that pass through a surface B A uniform magnetic field, B, passes through a plane surface of area A. Magnetic flux B A B Magnetic flux B A cos( ) Note: The flux can be negative! Physics 201: Lecture 1, Pg 24
Magnetic Flux The magnetic flux measures the amount of magnetic field passing through a loop of area A if the loop is tilted at an angle from the field. The SI unit of magnetic flux is the weber: 1 weber = 1 Wb = 1 T m 2 Physics 201: Lecture 1, Pg 25
The Area Vector Let s define an area vector to be a vector in the direction of, perpendicular to the surface, with a magnitude A equal to the area of the surface. Vector has units of m 2. Physics 201: Lecture 1, Pg 26
Magnetic Flux Through a Loop Physics 201: Lecture 1, Pg 27
Clicker Question 4: The metal loop is being pulled through a uniform magnetic field. Is the magnetic flux through the loop changing? A. Yes. B. No. Physics 201: Lecture 1, Pg 28
Clicker Question 5: The metal loop is being pulled through a uniform magnetic field. Is the magnetic flux through the loop changing? A. Yes. B. No. Physics 201: Lecture 1, Pg 29
Clicker Question 6: A conducting rod is sliding at a velocity v = 0.12 m/s on conducting rails. At time t = 0 the rod is at position l = 0.5 m (see picture). The entire device is placed in a uniform magnetic field B = 0.45 T directed into the page. The width w = 0.4 m. What is the magnetic flux Φ through the conducting loop at time t = 0? (a) Φ = 0 T-m 2 (b) Φ = 0.09 T-m 2 (c) Φ = 0.198 T-m 2 (d) Φ = 0.45 T-m 2 (e) Φ = 12 T-m 2 Physics 201: Lecture 1, Pg 30
Clicker Question 7: A loop of wire of area A is tipped at an angle to a uniform magnetic field B. The maximum flux occurs for an angle = 0. What angle will give a flux that is ½ of this maximum value? A. 30 B. 45 C. 60 D. 90 Physics 201: Lecture 1, Pg 31
Lenz s Law Physics 201: Lecture 1, Pg 32
Lenz s Law Pushing the bar magnet into the loop causes the magnetic flux to increase in the downward direction. To oppose the change in flux, which is what Lenz s law requires, the loop itself needs to generate an upward-pointing magnetic field. The induced current ceases as soon as the magnet stops moving. Physics 201: Lecture 1, Pg 33
Lenz s Law Pushing the bar magnet away from the loop causes the magnetic flux to decrease in the downward direction. To oppose this decrease, a clockwise current is induced. Physics 201: Lecture 1, Pg 34
Clicker Question 8: A magnetic field goes through a loop of wire, as below. If the magnitude of the magnetic field is increasing, what can we say about the current in the loop? A. The loop has a clockwise current. B. The loop has a counterclockwise current. C. The loop has no current. Physics 201: Lecture 1, Pg 35
Clicker Question 9: A magnetic field goes through a loop of wire, as below. If the magnitude of the magnetic field is decreasing, what can we say about the current in the loop? A. The loop has a clockwise current. B. The loop has a counterclockwise current. C. The loop has no current. Physics 201: Lecture 1, Pg 36
Clicker Question 10: 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 201: Lecture 1, Pg 37
Clicker Question 11: 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 201: Lecture 1, Pg 38