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1 Chapter 21 Magnet Forces and Magnetic Fields 2 1) Magnets and Magnetic Fields a) Natural permanent magnets – Like poles repel, unlike attract – come in pairs (no monopoles) – Interact with earth; define N (or north-seeking) pole as pole attracted to North pole of earth 3 b) Magnetic field direction: - direction of force on N pole B 4 c) Field of dipole 5 d) Magnetostatics for poles (identical to electrostatics for charges) – – – – – 2 types: N, S vs +,Unlike attract, like repel Inverse square law Force along joining line Magnetic Field: F B qM 6 e) Why study magnetism? – No monopoles (yet) – Poles (dipoles) produced by moving charges (no direct control of pole distribution) – Charges affected by magnetic field i.e. fundamental unit is still charge; want magnetic field due to charge, and force on charge due to magnetic field 7 2) Magnetic field due to current (direction) • Oersted (1820) 8 I B r 9 3) Magnetic force on current a) Orthogonal case Force per unit length F IB defines B Direction from RHR1: B fingers, I thumb, F palm 10 Units: F N B tesla (T) I Am Bearth .5 gauss 5 105 T Bfridge magnet .01T Bsuper conducing 110 T 11 b) General case Force per unit length F IBsin L 12 4) Force between parallel wires I1 B ; d F F I2 B I1I2 k d 13 FE + FB FB + v v FE Attraction or repulsion? Does it depend on reference frame? 14 - - + + - - + + - - + v + v 15 F I1I2 k d • Define Ampere as the quantity of current that produces a force per unit length of 2 x 10-7 N/m for separation of 1 m • Then (2 107 N/m)(1m) 7 2 k 2 10 N/A 2 (1A ) • This defines C and gives k 1 40 8.988 109 Nm2/C 2 16 • Permeability of free space 0 2k 4 10 N/A 7 Then F 0 I1I2 2 d 2 0 k 2 17 5) Field due to long straight wire (magnitude) I B r 0 I B 2 r 18 6) Force on a moving charge • Zero at rest • Zero parallel to B • Max perpendicular to B 19 • Proportional to component of v perp to B F qvBsin (Alternative definition of B) • Perpendicular to B • Perpendicular to v 20 7) Motion of a charge in a magnetic field a) Constant force motion is parabolic electric or gravitational field not everywhere perp to velocity not magnetic field 21 b) Constant magnitude perpendicular to motion radial field (circular motion) mass on a string motion is circular magnetic field produces circular motion (initial vel. perp. to B) Force due to the field: F qvB 22 For circular motion: 2 mv F Fc r So, mv r qB mv 2 qvB r r depends on v, B v qB r m angular freq. independent of speed, radius Tracks in a bubble chamber • electron-positron creation • 1, 3 positive • 2 negative • energy: 3 > 2 > 1 • energy decreases by collisions 23 24 Example: Find speed and radius for proton B = 0.10 T V = 2100 V 25 c) Work done by magnetic field Work by a force F F displacement, x W Fx cos For a magnetic field, 0 Work = 0 26 d) Velocity selector Force due to E (down): FE qE Force due to B (up): FB qvB For zero deflection, FE = FB : qE qvB E v B 27 e) Mass Spectrometer Ion energy: 2qV KE mv qV v m 1 2 Radius of motion: mv m 2qV r qB qB m r 2 m q 2V B m r 2B 2 q 2V