Chapter 19: Magnetic Fields PHY2054: Chapter 19 1 Magnetic Fields ÎMagnetic field (units, field lines) Magnetic ÎEffects field of the earth and other astronomical objects of magnetic fields on charges and currents Force on a moving charge Force on a current Torque on a current loop Path followed by particle in magnetic field ÎGenerating magnetic fields Long wire Current loop Solenoid ÎInstruments Mass spectrometers Cyclotrons and synchrotrons PHY2054: Chapter 19 2 Reading Quiz ÎThe magnetic force on a moving charged particle is: (1) (2) (3) (4) (5) Perpendicular to the velocity Parallel to the velocity Parallel to the B field Independent of the velocity None of the above PHY2054: Chapter 19 3 Reading Quiz Î Consider +q moving relative to a B field as shown. What is the direction of the magnetic force? Force Force Force Force is is is is parallel to v parallel to B into the page out of the page B +q PHY2054: Chapter 19 4 Reading Quiz ÎWhen I cut a magnet into two pieces I get: An isolated north and south magnetic pole Two smaller magnets The two pieces are no longer magnets PHY2054: Chapter 19 5 Bar Magnets ÎTwo poles: “north” and “south” ÎLike poles repel ÎUnlike poles attract ÎMagnetic S poles cannot be isolated N Similar to dipole field from electrostatics PHY2054: Chapter 19 6 Magnetic Monopoles? ÎCan any isolated magnetic charge exist? We would call this a “magnetic monopole” It would have a + or – magnetic charge ÎHow can we isolate this magnetic charge? Cut a bar magnet in half? NO! What you get is a bunch of little magnets! Magnetic monopoles have never been seen! PHY2054: Chapter 19 7 Searches for Magnetic Monopoles PHY2054: Chapter 19 8 Earth is a big magnet!! The North pole of a small magnet (compass) points towards geographic North because Earth’s magnetic South pole is up there!! Particles moving along field lines cause Aurora Borealis. http://science.nasa.gov/spaceweather/aurora/gallery_01oct03.html PHY2054: Chapter 19 9 What Causes Magnetism? ÎWhat is the origin of magnetic fields? Electric charge in motion! For example, a current in a wire loop produces a field very similar to that of a bar magnet (as we shall see). ÎUnderstanding the source of bar magnet field lies in understanding currents at the atomic level within matter Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect) PHY2054: Chapter 19 10 Magnetic Field Units ÎFrom the expression for force on a current-carrying wire: B = Fmax / I L Units: Newtons/A⋅m ≡ Tesla (SI unit) Another unit: 1 gauss = 10-4 Tesla ÎSome sample magnetic field strengths: Earth: B = 0.5 gauss = 0.5 x 10-4 T Galaxy: B ∼ 10-6 gauss = 10-10 T Bar magnet: B ∼ 100 – 200 gauss Strong electromagnet: B = 2 T Superconducting magnet: B = 5 – 10 T Pulse magnet: B ∼ 100 T Neutron star: B ∼ 108 – 109 T Magnetar: B ∼ 1011 T PHY2054: Chapter 19 11 Pulsars Rapidly Rotating Neutron Stars Enormous Magnetic Fields Beam off Beam on Crab Pulsar R = 10 km M = 1.4 solar mass B ≈ 108 T Period = 1/30 sec PHY2054: Chapter 19 12 Magnetic Force on Moving Charge ÎMagnetic force F = qvB sin φ ÎSign of charge Force is in opposite direction from positive charge ÎForce magnitude depends on direction of v relative to B v is parallel to B ⇒ sinφ = 0 F =0 F = qvB v is perpendicular to B ⇒ sinφ = 1 F = qvB sin 45 v is at angle 45° to B ⇒ sinφ = 0.71 ÎForce direction is perpendicular to both B and v Right hand rule (next slide) PHY2054: Chapter 19 13 Right Hand Rule For Magnetic Force ÎFirst point fingers in direction of velocity Curl fingers toward B field ⇒ Thumb points toward force v F B v +q B F is into page PHY2054: Chapter 19 14 Example with m = 1.5 g, q = −2μC moves with velocity 2,000 m/s through a magnetic field of 2.5 T at an angle of 30° to the field. ÎParticle Magnitude of force ( ) F = qBv sin φ = 2 × 10−6 ( 2.5)( 2000 )( 0.5) = 0.005 N Direction of force: up out of the page. Use RHR and take opposite direction because of −q v B −q F is up out of page PHY2054: Chapter 19 15 Quiz ÎA charged particle moves in a straight line through some region of space. Can you conclude that B = 0 here? (1) Yes (2) No A B field can exist since if v || B there is no magnetic force PHY2054: Chapter 19 16 Magnetic Force ÎA negative particle enters a magnetic field region. What path will it follow? (1) (2) (3) (4) (5) A B C D E x x x x x x x x x x x x A x x x x x x x x x x x x B 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 x x x x x x x x x x x x x x x x C D E (1) RHR says it bends down (− charge) (2) But force cannot instantaneously change v and the velocity vector bends continuously (3) So the answer is D, not E PHY2054: Chapter 19 17 Magnetic Force on Current-Carrying Wire ÎMagnitude of force on current F = ( force on one charge ) × ( # of charges ) = ( evd B sin φ ) × ( ne AL ) = ( ene vd A ) BL sin φ = iBL sin φ ÎDirection of force: RHR PHY2054: Chapter 19 18 Example ÎA 4 m long wire carries current of 500A in NE direction Magnitude φ of force (B = 0.5 gauss = 5 × 10-5 T, pointing N) = 45° ( ) F = iBL sin 45° = ( 500 ) 5 × 10−5 ( 4 )( 0.71) = 0.071N Direction ÎCan of force: Upwards, from RHR adjust current in wire to balance against gravity Calculate mass from density, length and cross-sectional area iBL sin φ = mg m = ρ LA = density × volume ρ Ag i= B sin φ PHY2054: Chapter 19 19 Magnetic Force ÎA vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire? (a) left (b) right (c) zero (d) into the page (e) out of the page B I is parallel to B, so no magnetic force I PHY2054: Chapter 19 20