PHY2054: Chapter 191Chapter 19: Magnetic FieldsPHY2054: Chapter 192Magnetic Fields ÎMagnetic field (units, field lines) Magnetic field of the earth and other astronomical objectsÎEffects 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 fieldÎGenerating magnetic fields Long wire Current loop SolenoidÎInstruments Mass spectrometers Cyclotrons and synchrotronsPHY2054: Chapter 193Reading QuizÎThe magnetic force on a moving charged particle is: (1) Perpendicular to the velocity (2) Parallel to the velocity (3) Parallel to the B field (4) Independent of the velocity (5) None of the abovePHY2054: Chapter 194Reading QuizÎ Consider +q moving relative to a B field as shown. What is the direction of the magnetic force? Force is parallel to v Force is parallel to B Force is into the page Force is out of the pageB+qPHY2054: Chapter 195Reading QuizÎWhen 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 magnetsPHY2054: Chapter 196Bar MagnetsÎTwo poles: “north” and “south”ÎLike poles repelÎUnlike poles attractÎMagnetic poles cannot be isolated NSSimilar to dipole field from electrostaticsPHY2054: Chapter 197Magnetic Monopoles?ÎCan any isolated magnetic charge exist? We would call this a “magnetic monopole” It would have a + or – magnetic chargeÎHow can we isolate this magnetic charge? Cut a bar magnet in half? NO!Magnetic monopoles have never been seen!What you getis a bunch oflittle magnets!PHY2054: Chapter 198Searches for Magnetic MonopolesPHY2054: Chapter 199Earth 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.htmlPHY2054: Chapter 1910What 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 matterOrbits of electrons about nucleiIntrinsic “spin” of electrons (more important effect)PHY2054: Chapter 1911Magnetic Field UnitsÎFrom the expression for force on a current-carrying wire: B = Fmax/ I L Units: Newtons/A⋅m ≡ Tesla (SI unit) Another unit: 1 gauss = 10-4TeslaÎSome sample magnetic field strengths: Earth: B = 0.5 gauss = 0.5 x 10-4 T Galaxy: B ∼ 10-6gauss = 10-10T 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 ∼ 108–109T Magnetar: B ∼ 1011TPHY2054: Chapter 1912PulsarsRapidly Rotating Neutron StarsEnormousMagnetic FieldsBeam off Beam onCrab PulsarR = 10 kmM = 1.4 solar massB ≈ 108TPeriod = 1/30 secPHY2054: Chapter 1913Magnetic Force on Moving ChargeÎMagnetic forceÎSign of charge Force is in opposite direction from positive chargeÎForce magnitude depends on direction of v relative to B v is parallel to B ⇒ sinφ = 0 v is perpendicular to B ⇒ sinφ = 1 v is at angle 45° to B ⇒ sinφ = 0.71ÎForce direction is perpendicular to both B andv Right hand rule (next slide)sinFqvBφ=FqvB=0F=sin45FqvB=PHY2054: Chapter 1914Right Hand Rule For Magnetic ForceÎFirst point fingers in direction of velocity Curl fingers toward B field ⇒ Thumb points toward forceFvBB+qvF is into pagePHY2054: Chapter 1915ExampleÎParticle 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. Magnitude of force Direction of force: up out of the page. Use RHR and take opposite direction because of −q()()()()6sin 2 10 2.5 2000 0.5 0.005NFqBvφ−==× =B−qvF is up out of pagePHY2054: Chapter 1916QuizÎA charged particle moves in a straight line through some region of space. Can you conclude that B = 0 here? (1) Yes (2) NoA B field can exist since if v || Bthere is no magnetic forcePHY2054: Chapter 1917ÎA negative particle enters a magnetic field region. What path will it follow? (1) A (2) B (3) C (4) D (5) Ex x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xMagnetic Force ABCDE(1)RHR says it bends down (− charge)(2)But force cannot instantaneously change vand the velocity vector bends continuously(3)So the answer is D, not EPHY2054: Chapter 1918Magnetic Force on Current-Carrying WireÎMagnitude of force on currentÎDirection of force: RHR()()()()()force on one charge # of chargessin sin sindeedFev B n AL en v A BL iBLφφφ=×=×= =PHY2054: Chapter 1919ExampleÎA 4 m long wire carries current of 500A in NE direction Magnitude of force (B = 0.5 gauss = 5 × 10-5T, pointing N) φ = 45° Direction of force: Upwards, from RHRÎCan adjust current in wire to balance against gravity Calculate mass from density, length and cross-sectional areasiniBL mgφ=()()()( )5sin45 500 5 10 4 0.71 0.071NFiBL−=°=× =density volumemLAρ== ×sinAgiBρφ=PHY2054: Chapter 1920Magnetic 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 IBI is parallel to B, sono magnetic
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