Magnetic fields & forces

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Percival Richardson
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1 Phys 102 Lecture 10 Magnetic fields & forces 1

2 Today we will... Learn about the magnetism Magnetic field B Magnetic force F on moing charge Apply these concepts! Charged particle motion in a magnetic field Mass spectrometry Earth s magnetic field & northern/southern h lights Phys. 102, Lecture 10, Slide 2

3 Electricity s. magnetism Electricity Positie & negatie charge Opposite charges attract, like charges repel Magnetism N & S poles N & S always together as dipole (NO magnetic charge ) Opposite poles attract, like poles repel N S N S N S S N S N N S DEMO Phys. 102, Lecture 10, Slide 3

4 Electric field Electricity s. magnetism E Magnetic field Vector at location in space Vector at location in space Points from positie & negatie Q Points from Nto S pole Units: N/C = V/m Units: T ( Tesla ) B + Electric dipole E field Magnetic dipole B field Phys. 102, Lecture 10, Slide 4

5 Sources of magnetic fields There is no magnetic charge, so where do magnetic fields come from? + Geodynamo Moing electric charge (current) Intrinsic magnetic dipole ( spin ) Phys. 102, Lecture 10, Slide 5

6 Magnetic force Magnetic field B exerts a force on a moing charge q: F = q Bsin θ Angle between and B Speed of charge q Magnetic field strength Right hand rule (RHR) B θ q + F Thumb along B Fingers along B F on + q is out of palm F on q is into palm F is to both and B Phys. 102, Lecture 10, Slide 6

7 ACT: Right hand rule practice A + charge moing to the right in a uniform B field experiences a force F up. Which way does the B field point? q F + A. Up B. Down C. Into the page D. Out of the page Phys. 102, Lecture 10, Slide 7

8 ACT: Right hand rule practice A charge moing out of the page in a uniform B field to the left experiences a force F inwhich direction? A. Up B. Down B q C. Into the page D. Out of the page DEMO Phys. 102, Lecture 10, Slide 8

9 ACT: Moing charges The three charges below hae equal charge and speed, but are traeling in different directions in a uniform magnetic field. B Which particle experiences the greatest magnetic force? A. 1 B. 2 C. 3 D. All same The force on charge 3 is in the same direction as the force on 1 A. True B. False Phys. 102, Lecture 10, Slide 9

10 Checkpoint 1.1 Each chamber has a unique magnetic field. A positiely charged particle enters chamber 1 with elocity 75 m/s up, and follows the dashed trajectory = 75 m/s q = +25 mc What is the direction of the force on the particle just as it enters region 1? A. up B. down C. left D. right E. into page F. out of page Phys. 102, Lecture 10, Slide 10

11 Checkpoint 1.2 Each chamber has a unique magnetic field. A positiely charged particle enters chamber 1 with elocity 75 m/s up, and follows the dashed trajectory = 75 m/s q = +25 mc What is the direction of the magnetic field in region 1? A. up B. down C. lf left D. right E. into page F. out of page Phys. 102, Lecture 10, Slide 11

12 ACT: Checkpoint 1.4 Each chamber has a unique magnetic field. A positiely charged particle enters chamber 1 with elocity 75 m/s up, and follows the dashed trajectory = 75 m/s q = +25 mc What is the direction of the magnetic field in region 2? A. up B. down C. lf left D. right E. into page F. out of page Phys. 102, Lecture 10, Slide 12

13 ACT: Checkpoint 1.5 Each chamber has a unique magnetic field. A positiely charged particle enters chamber 1 with elocity 75 m/s up, and follows the dashed trajectory = 75 m/s q = +25 mc How do the magnitudes of the B fields in region 1 and 2 compare? A. B 1 > B 2 B. B 1 = B 2 C. B 1 < B 2 Phys. 102, Lecture 10, Slide 13

14 Motion in uniform B field Charged particle moes along x to B field Particle moes in a circle + F R B field does no work (since F d) y B Kinetic energy is constant Speed is constant x DEMO Phys. 102, Lecture 10, Slide 14

15 Mass spectrometer Mass spectrometry uses a B field to analyze chemical compounds Compound is aporized into fragments & ionized, accelerated with a E field into a B field Fragments separate according to mass to charge ratio (m/q) Phys. 102, Lecture 10, Slide 15

16 Calculation: Mass spectrometer A mass spectrometer is used to separate different isotopes of carbon. Carbon ions are accelerated to a speed = 10 5 m/s; assume all hae charge +1e = C. Find which C isotope traels along the green dotted path to the detector. FA13 EX2 = 10 5 m/s R = 6.8 cm B = 02T C + m R = qb qbr m = = = kg 5 10 =13amu 27 1amu = kg 13 C + Which way does the B field point? Phys. 102, Lecture 10, Slide 16

17 ACT: Mass spectrometer I Magnet The mass spectrometer isolates C ion beam three C isotopes a, b, c. They moe at a speed = 10 5 m/s = 10 5 m/s a entering the B field and follow the dashed dpaths. R c b Detector How do the speeds of the different isotopes a, b, c leaing the B field compare? A. a > b > c B. a = b = c C. a < b < c Phys. 102, Lecture 10, Slide 17

18 ACT: Mass spectrometer II Magnet The mass spectrometer isolates C ion beam three C isotopes a, b, c. They moe at a speed = 10 5 m/s = 10 5 m/s a entering the B field and follow the dashed dpaths. R c b Detector How do the masses of the different isotopes a, b, c compare? A. m a > m b > m c B. m a = m b = m c C. m a < m b < m c Phys. 102, Lecture 10, Slide 18

19 3 D motion in uniform B field What if particle has a component along B? Charged particle moes in x z plane, B field along z B + + F B = z B z y + x x x + F = 0 F = qb Component to B Component to B remains constant rotates in a circle R y = m qb Charge moes in a helical trajectory Phys. 102, Lecture 10, Slide 19

20 Aurora borealis & australis Earth s B field protects against stream of ions from sun ( solar wind ) z B x y Aurora australis Southern lights B field directs ions to atmosphere in north and south hemispheres. Ions collide with particles in atmosphere and emit light: aurora Phys. 102, Lecture 10, Slide 20

21 Summary of today s lecture Electric s. magnetic forces Force: Electric Magnetic Source: Charge Moing charge Act on: Charge Moing charge Magnitude: F E = q E F B = q B sin(θ) Direction: to E to, B Work: W E = qed cos(θ) W B = 0 Phys. 102, Lecture 10, Slide 21

22 B F B F F B B F Phys. 102, Lecture 10, Slide 22

Magnetic Fields & Forces

Magnetic Fields & Forces Oersted discovered that an electric current will produce a magnetic field around conductor only a moving charge creates a magnetic field the magnetic field is circular around the