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Chapter 24 Magnetic Fields and Forces Topics: • • • • • Magnets and the magnetic field Electric currents create magnetic fields Magnetic fields of wires, loops, and solenoids Magnetic forces on charges and currents Magnets and magnetic materials Sample question: This image of a patient’s knee was made with magnetic fields, not x rays. How can we use magnetic fields to visualize the inside of the body? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-1 Checking Understanding Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P? Slide 24-19 Answer Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P? Slide 24-20 Electric Currents Also Create Magnetic Fields A long, straight wire A current loop Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A solenoid Slide 24-15 The Magnitude of the Field due to a Long, Straight, Current-Carrying Wire 0 I B 2 r 0 permeability constant 1.257 10 T m/A 6 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-25 The Magnetic Field of a Current Loop B 0 I 2R Magnetic field at the center of a current loop of radius R B 0 NI 2R Magnetic field at the center of a current loop with N turns Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-29 Checking Understanding The diagram below shows a current loop perpendicular to the page; the view is a “slice” through the loop. The direction of the current in the wire at the top and the bottom is shown. What is the direction of the magnetic field at a point in the center of the loop? A. B. C. D. To the left Up To the right Down Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-35 Answer The diagram below shows a current loop perpendicular to the page; the view is a “slice” through the loop. The direction of the current in the wire at the top and the bottom is shown. What is the direction of the magnetic field at a point in the center of the loop? A. B. C. D. To the left Up To the right Down Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-36 The Magnetic Field Inside a Solenoid N B 0 I L Magnetic field inside a solenoid of length L with N turns. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-31 Example What is the direction and magnitude of the magnetic field at point P, at the center of the loop? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-30 Right Hand Rules for Magnetism • Right-hand rule 1 (RHR 1) => for finding magnetic force FB= q*v_vector x B_vector (Cross-Product Rule) 1. Point right hand in the direction the charges are moving (current or velocity) 2. Rotate your right hand until you can point your fingers in the direction of the magnetic Field 3. Thumb points in direction of force for + charge Force is in opposite direction for - charges • Right-hand rule 2 (RHR 2) => Finding direction of B from I • • Point thumb of right hand in direction of current I, B-field lines curl in direction of fingers • Right-hand rule 3 (RHR 3) => Finding direction of current in a loop from direction of B-field • • Point thumb of right hand in direction of B-field Fingers of right hand curl in direction of current Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-2 The Force on a Charged Particle Moving in a Magnetic Field Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-32 The Right-Hand Rule for Forces Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-33 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-34 Paths of Charged Particles in Magnetic Fields mv r qB Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-35 The Mass Spectrometer Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-36 Velocity Selector Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-37 Magnetic Fields Exert Forces on Currents Fwire ILB Magnitude of the force on a current segment of length L perpendicular to a magnetic field Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-37 Forces between Currents Magnetic force between two parallel current-carrying wires Fparallel wires Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 0 LI1 I 2 2d Slide 24-38 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-39 Checking Understanding The magnetic field at point P is zero. What are the magnitude and direction of the current in the lower wire? A. B. C. D. E. F. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 10 A to the right. 5 A to the right. 2.5 A to the right. 10 A to the left. 5 A to the left. 2.5 A to the left. Slide 24-27 Answer The magnetic field at point P is zero. What are the magnitude and direction of the current in the lower wire? E. 5 A to the left. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-28 Forces between Current Loops Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-40 A Current Loop Acts like a Bar Magnet Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-41 Checking Understanding The diagram below shows slices through two adjacent current loops. Think about the force exerted on the loop on the right due to the loop on the left. The force on the right loop is directed A. B. C. D. to the left. up. to the right. down. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-37 Answer The diagram below shows slices through two adjacent current loops. Think about the force exerted on the loop on the right due to the loop on the left. The force on the right loop is directed A. B. C. D. to the left. up. to the right. down. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-38 Additional Questions 1. A loop carrying a current as shown rests in a uniform magnetic field directed to the right. If the loop is free to rotate, A. B. C. it will rotate clockwise. it will not rotate. it will rotate counterclockwise. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-66 Answer 1. A loop carrying a current as shown rests in a uniform magnetic field directed to the right. If the loop is free to rotate, A. B. C. it will rotate clockwise. it will not rotate. it will rotate counterclockwise. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-67