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Chapter 27 Magnetic Field and Magnetic Forces PowerPoint® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Copyright © 2012 Pearson Education Inc. Modified 2016 Scott Hildreth Chabot College Goals for Chapter 27 • Study magnets & forces they exert on each other • Calculate force a magnetic field exerts on a moving charge • Contrast magnetic field lines with electric field lines • Analyze motion of a charged particle in a magnetic field Goals for Chapter 27 • See applications of magnetism in physics and chemistry • Analyze magnetic forces on current-carrying conductors • Study the behavior of current loops in a magnetic field Introduction • How does magnetic resonance imaging (MRI) allow us to see details in soft nonmagnetic tissue? • How can magnetic forces, which act only on moving charges, explain the behavior of a compass needle? Magnetic poles • Forces between magnetic poles mimic forces between charges. Magnetism and certain metals • BUT….either pole of a permanent magnet will attract a metal like iron?? Magnetic field of the earth Magnetic monopoles • Breaking a bar magnet does not separate its poles • There is no experimental evidence for magnetic monopoles. Electric current and magnets • (1820) Hans Oersted discovered wire carrying current causes compass to deflect. • There is a connection between moving charges and magnetism. Hans Oersted • Father owned a pharmacy • Brother became prime minister of Denmark • Received 3-year travel grant to explore science in Europe • Accomplished in more than physics! • • Thesis based on Kant: “Architectonics of Natural Metaphysics” First to produce pure aluminum The Oersted Medal for teaching of physics! Electric current and magnets • RIGHT-HAND RULE applies to identify direction of magnetic field from currentcarrying wire! Right Thumb in direction of current Right Hand Fingers curl in direction of Magnetic field! Electric current and magnets • We’ll find a RIGHTHAND RULE applies to identify the direction of a magnetic field from a current-carrying wire! Right Thumb in direction of current Right Hand Fingers curl in direction of Magnetic field! The magnetic field • A moving charge (or current) creates a magnetic field in the surrounding space. The magnetic field • Magnetic fields denoted with letter “B” • measured in Tesla or Gauss (10-7 Tesla) The magnetic field • Magnetic fields denoted with letter “B” • measured in Tesla or Gauss (10-4 Tesla) • Tesla = Newton-second Coulomb-meter • Tesla = Newton/Amp-meter The magnetic field • A magnetic field exerts a force on any other moving charge - or current - that is present in the field. The magnetic force on a moving charge • Magnetic force on moving charge q is perpendicular to both • velocity vector direction of q and • magnetic field. • Magnitude of magnetic force is F = |q|vB sin. Magnetic force as a vector product • Write magnetic force as vector cross product • Right-hand rule gives direction of force on positive charge. Magnetic force as a vector product • Write magnetic force as vector cross product • Left-hand rule gives direction of force on negative charge. Equal velocities but opposite signs • Two charges of equal magnitude but opposite signs moving in same direction in same field experience magnetic forces in opposite directions. Cathode Ray Tubes! • The first computer “monitors” Determining the direction of a magnetic field • Cathode-ray tube shows direction of magnetic field Magnetic force on a proton • Beam of protons (q =+1.6 x 10-19C) moves at 3.0 x 105 m/s through 2.0 Tesla field directed along z axis. Velocity direction is 30 degrees from the z axis in the x-y plane. Force on a proton? Magnetic force on a proton • Beam of protons (q =+1.6 x 10-19C) moves at 3.0 x 105 m/s through 2.0 Tesla field directed along z axis. Velocity direction is 30 degrees from the z axis in the x-y plane. Force on a proton? • F = qv x B = (1.6 x 10-19 C) x (3 x 105 m/s) x (2 T) x sin (30) • = 4.8 x 10-14 N Magnetic field lines Magnetic field lines are not lines of force • Important! Remember magnetic field lines are not lines of magnetic force. Magnetic flux Magnetic flux calculations • Flux through flat surface of area 3.0 cm2 = +0.90 mWb • “mWb = “milli-Webers” • What is B field and direction of A? Magnetic flux calculations • Flux through flat surface of area 3.0 cm2 = +0.90 milliWb. • What is B field and direction of A? • Flux FB = BA cos = +0.90 milliWb • A = 3.0 cm2 = 3.0 x 10-4 m2 and = 60° • B = 6.0 Teslas Motion of charged particles in a magnetic field • Charged particle in magnetic field (only) moves with constant speed • F = qv x B • Force is PERPENDICULAR to v • So is acceleration! • No change in magnitude of velocity! Motion of charged particles in a magnetic field • If velocity of particle is ONLY perpendicular to B field, particle moves in a circle of radius R = mv/|q|B. • Number of revolutions of particle per unit time is cyclotron frequency. Motion of charged particles in a magnetic field • F = qvB = mv2/R w = v/R = qB/m f = w/2p Motion of charged particles in a magnetic field • If velocity of particle is perpendicular to B field, particle moves in a circle of radius R = mv/|q|B. • IF add a “kick” to speed, Radius increases! • A cyclotron! • Number of revolutions of particle per unit time is cyclotron frequency. The “father” of cyclotrons! Ernest Lawrence Motion of charged particles in a magnetic field Motion of charged particles in a magnetic field • Magnetron in Microwave Oven! Motion of charged particles in a magnetic field • Magnetron in Microwave Oven! Motion of charged particles in a magnetic field • Magnetron in Microwave Oven! Motion of charged particles in a magnetic field • Magnetron in Microwave Oven! Helical motion • If particle has velocity components parallel to and perpendicular to B field, its path is a helix. • Speed & kinetic energy still particle remain constant. A nonuniform magnetic field • Charges can be trapped in a magnetic bottle, which results from a non-uniform magnetic field. • Van Allen radiation belts act like a magnetic bottle, and produce aurora. These belts are due to the earth’s non-uniform field. Bubble chamber • Track of charged particles in a bubble chamber experiment. Velocity selector • Velocity selectors use perpendicular electric & magnetic fields to select particles of specific speed from beam. • Only particles having speed v = E/B pass through undeflected. Thomson’s e/m experiment • Measure ratio e/m for electron. Mass spectrometer • Mass spectrometer measures masses of ions. • Bainbridge mass spectrometer first uses velocity selector, then magnetic field separates particles by mass. The magnetic force on a current-carrying conductor • Magnetic force on a moving positive charge in a conductor. • F = Il x B = ILB sin • dF = Idl x B for a segment dl • VECTORS! • • I = scalar current (amps) • l = direction of current • B = direction of Mag. Field. Magnetic force is perpendicular to the wire segment and the magnetic field. Magnetic force on a straight conductor • Example 27.7 A straight horizontal copper rod carries a current of 50.0 A from west to east in a region between the poles of a large electromagnet. In this region there is a horizontal magnetic field towards the northeast (45 degrees north of east) with magnitude 1.20 T. Magnetic force on a straight conductor • Example 27.7 A straight horizontal copper rod carries a current of 50.0 A from west to east in a region between the poles of a large electromagnet. In this region there is a horizontal magnetic field towards the northeast (45 degrees north of east) with magnitude 1.20 T. • What is F on the segment? • What is the maximum possible force if it changes direction? Magnetic force on a straight conductor • Example 27.7 A straight horizontal copper rod carries a current of 50.0 A from west to east in a region between the poles of a large electromagnet. In this region there is a horizontal magnetic field towards the northeast (45 degrees north of east) with magnitude 1.20 T. • What is F on the segment? • What is the maximum possible force if it changes direction? Magnetic force on a straight conductor • Example 27.7 A straight horizontal copper rod carries a current of 50.0 A from west to east in a region between the poles of a large electromagnet. In this region there is a horizontal magnetic field towards the northeast (45 degrees north of east) with magnitude 1.20 T. • What is F on the segment? • What is the maximum possible force if it changes direction? How do we solve physics problems? - SKETCH it - COMB through the problem; pickout key data points and concepts - Set up what is known, and what is needed! Magnetic force on a straight conductor A straight horizontal copper rod carries a current of 50.0 A from west to east in a region between the poles of a large electromagnet. 50.0 A W E Magnetic force on a straight conductor • What is Force on the current segment from the magnetic field? • What is the maximum possible force if it changes direction? Magnetic force on a straight conductor • F = iL x B = iLB (sin q) • Direction of F is perpendicular to both (Right-Hand Rule) Magnetic force on a straight conductor • F = iL x B = iLB (sinq) • If F = mg, current is large enough to hold up conductor Magnetic force on a curved conductor • Look at Example 27.8! • What is the TOTAL magnetic force on this wire? Loudspeaker • Loudspeaker design. • If current in the voice coil oscillates, speaker cone oscillates at the same frequency. Force and torque on a current loop in B field • Net force on a current loop in a uniform magnetic field is zero. • But the net torque is not, in general, equal to zero. Force and torque on a current loop • Net force on a current loop in a uniform magnetic field is zero. • But the net torque is not, in general, equal to zero. Force and torque on a current loop • Net force on a current loop in a uniform magnetic field is zero. • But the net torque is not, in general, equal to zero. The direct-current motor • Direct-current motor. The direct-current motor • Direct-current motor. The direct-current motor • Direct-current motor. The direct-current motor • Direct-current motor. Real life! • Inertia of coil • Resistance of wire • Eddy effects of nonlinear magnetic field • Load on shaft Magnetic torque & magnetic moment • Right-hand rule to determines direction of magnetic moment (turning force = torque) on current loop. Magnetic torque and potential energy of a coil • Potential energy of magnetic dipole in a magnetic field. How magnets work How magnets work The Hall Effect • Hall effect