Download Lecture 12: Magnetic Forces and Fields in Physics 202 and more Assignments Physics in PDF only on Docsity! 1 Physics 202, Lecture 12 Today’s Topics Magnetic Forces (Ch. 29) Review: magnetic force, magnetic dipoles Motion of charge in uniform B field: Applications: cyclotron, velocity selector, Hall effect Sources of the Magnetic Field (Ch. 30, part 1) Calculating the B field due to currents (Biot-Savart) Homework #5: due 10/15 ,10 PM. Optional reading quiz: due 10/12, 7 PM Magnetic Fields and Forces: Recap Magnetic Force: experienced by moving charges Magnetic Field B: sourced by moving charges direction: as indicated by north pole of compass ! F = q ! v ! ! B ! F = I d ! l ! ! B" (point charges) (currents) Field lines: closed loops! Outside magnet: N to S Inside magnet: S to N Units: 1 Tesla (T) = 1 N/(A m) 2 Torque on Current Loop in Uniform B field Force and torque on current loop: magnetic dipole moment: Loop rotates to minimize I.e., until µ B ! F net = 0, ! ! net = ! µ " ! B I I I I 1 2 3 4 B X • ! µ = NI ! A ! µ " ! B U = ! ! µi ! B (N=# of turns of loop, A=area) Charged Particle in Uniform B Field x x x x x x x x x x x x x x x x x x v B q x x x x x x x x x x x x x x x x x x FFv R Magnetic force does no work on charge: kinetic energy constant Force perpendicular to velocity: uniform circular motion ! F = q ! v ! ! B = m ! a 5 Application: Cyclotron First Modern Particle Accelerator First Cyclotron (1934) Lawrence & Livingston Fixed Frequency Application: Velocity, Mass Selectors Velocity and mass selector: Velocity Selector Mass Selector speed selected: mass selected: v = E B m q = rB 0 v = rB 0 (E B) 6 The Hall Effect (1) positive charges moving counterclockwise: upward force, upper plate at higher potential negative charges moving clockwise: upward force Upper plate at lower potential Equilibrium between electrostatic & magnetic forces: Potential difference on current-carrying conductor in B field: F up = qv d B F down = qE ind = q V H w V H = v d Bw = "Hall Voltage" The Hall Effect (2) VH = vdBw = IB nqt I = nqvdA = nqvdwt R H ! V H IB = 1 nqt Hall coefficient: Hall effect: determine sign,density of charge carriers (first evidence that electrons are charge carriers in most metals) 7 Magnetic Fields of charges, currents Are there analogous equations for the Magnetic Field? Two Ways to calculate the electric field: "Brute force" – Coulomb’s Law "High symmetry" – Gauss’ Law d ! E = k dq r 2 r̂ ! E id ! A! = q in " 0 Review: back to electrostatics: Calculation of Magnetic Fields (Currents) × I – Biot-Savart Law (“Brute force”) –AMPERIAN LOOP – Ampere’s Law (“High symmetry”) ! B id " l = µ 0#! I Two Ways to calculate the magnetic field: (Tuesday’s lecture) d ! B = µ 0 I 4! d ! l ! r̂ r 2
