Last time MAGNETIC FORCE point charge

Transcription

1 Last time MAGNTIC FORC point chage Result of Coss Poduct is Pependicula to both and Right-Hand Rule: 1) ) 1

2 Magnet foce on cuents Hall effect Relatiity effect Today

3 iclicke Question Small metal ball has chage q +.5C and mass, m.5kg. Ball entes a egion of magnetic field B.5 T that is pependicula to its elocity m/s. Centipetal acceleation /. What is adius of the cue ball will moe thu in magnetic field? A. m B. 1m C. 5m D. 1m. 5m ẑ yˆ ˆx B Bxˆ ŷ 3

4 ẑ yˆ ˆx B Bxˆ ŷ a) F q 1 B (.5)()(.5) 5N b) (see diagam) Foce in z diection c) F ma q 1 B 5N a 5N/.5kg m/s d) / m/s, /(m/s ) (m/s) /m/s m 4

5 Biot-Saat Law BIOT-SAVART LAW point chage We need to undestand how these ae elated BIOT-SAVART LAW cuent in a wie length of this chunk of wie 5

6 GOAL: Show (point chage) (wie) (POSITIV) POINT CHARG MANY POINT CHARGS N paticles CHUNK OF WIR ΔV paticles pe olume ΔV Moe the ecto symbol length of this chunk of wie 6

7 Magnetic Foce on a chage o wie MAGNTIC FORC point chage We just showed how these ae elated MAGNTIC FORC cuent in a wie length of this chunk of wie 7

8 Magnetic Foce on a Wie Cuent-caying wie in an applied magnetic field B B applied B applied I Which way will the wie moe? 8

9 Vey Close to the Wie Vey close to the wie: << L CLOS TO TH WIR B I 9

10 iclicke question: Two long paallel wies cay cuents of 5 A and 1 A in the same diection as shown. What is the diection of the magnetic foce acting on the 1-A wie? a) Pependicula to the plane of the page and into the page b) Pependicula to the plane of the page and out of the page c) Upwad d) Downwad e) Inwad towad the othe wie f) Outwad away fom the othe wie 1

11 Foce Between Paallel Wies B applied Magnetic field applied by the ed wie. Blue wie feels a foce down. B applied I B applied F on blue wie I What about ecipocity? (qual and opposite foces) 11

12 iclicke question: Two long paallel wies cay cuents of 5 A and 1 A in opposite diections as shown. What is the diection of the magnetic foce on the 1-A wie? a) Pependicula to the plane of the page and into the page b) Pependicula to the plane of the page and out of the page c) Upwad d) Downwad e) Inwad towad the othe wie f) Outwad away fom the othe wie 1

13 Foce Between (Anti) Paallel Wies B applied Magnetic field applied by the ed wie. Blue wie feels a foce up. x B applied F on blue wie I x B applied x B applied I F on ed wie x B applied B applied Magnetic field applied by the blue wie. Red wie feels a foce down. 13

14 Hall ffect By measuing the Hall effect fo a paticula mateial, we can detemine the sign of the moing paticles that make up the cuent Why would it be anything othe than electons? (Negatie chages) Semiconductos: sometimes cuent is caied by electons, but sometimes it is caied by the "holes". In semiconductos, "holes" (missing electons) in the electon sea behae like positie chages. 14

15 Hall ffect MAGNTIC FORC point chage A hole in the electon sea behaes like a poton. Poton o "Hole" Inside a Mateial: Moing holes get pushed to the top x B applied x B applied lecton Moing electons get pushed to the bottom 15

16 Hall ffect MAGNTIC FORC point chage A hole in the electon sea behaes like a poton. Moing holes get pushed to the top Moing electons get pushed to the bottom Inside a Mateial: x B applied ΔV Hall Voltage How long does this go on? Until the Hall Voltage is stong enough to balance the magnetic foce ΔV Hall Voltage 16

17 Measuing the Hall ffect 1. Apply B-Field. Apply Cuent I 3. Measue "Hall Voltage" 17

18 Cuents Due to Magnetic Foces Metal ba F q + q F m -e ( ) B B polaization F m How much foce do we need to apply to keep the ba moing at constant speed? 18

19 Moing Ba and negy Conseation PIVI(emf) Ae we getting something fo nothing? F I F Ba cuent I: F I Il B -F F I ILB F m Wok: W Fx ILBx emf BL x Powe: Main pinciple of electic geneatos: Mechanical powe is coneted to electic powe P P P W t ILB ILB I(emf ) 19 x t

20 Refeence Fame B m q ˆ 4p Any magnetic field? B m q ˆ 4p ¹ chaged tape

21 iclicke Question Jessie Jack chaged tape In case Jack hae two positiely changed tapes side by side. Fo the inteaction between the two tapes : A). Jack and Jessie: puely though foce. B). Jack: only though foce. Jessie: only though B foce. C). Jack and Jessie: though a mixtue of B and foces. D). Jack: though only foces. Jessie: though a mixtue of B and foces. 1

22 Magnetic Foces in Moing Refeence Fames Two potons +e 1 +e F 1,m B 1 1 F 1,e lectic foce: (assume independent of fame?) 1 e F e q ˆ 1, 1 4pe Magnetic field: m q1 1 B1 4p Magnetic foce: q ˆ F1, m B1 F1, m q B 1 m e 4p

23 Magnetic Foces in Moing Refeence Fames +e 1 +e 1 e lectic foce: F1, e 4pe m e F 1,m Magnetic foce: F1, m 4p B 1 1 Ratio: F F 1, m 1, e æ m ö æ e 1 e ç / ç è 4p ø è 4pe ö ø F 1,e F 1,m ( m e ) F 1,e F F 1, m 1, e c 3

24 Magnetic Foces in Moing Refeence Fames +e 1 +e F 1,m B 1 F F 1, m 1, e Fo <<c the magnetic foce is much smalle than electic foce c 1 F 1,e How can we detect the magnetic foce on a cuent caying wie? 1 e æ ö Full Loentz foce: F F1, e - F1, m ç1-4pe è c ø downwad 4

25 Magnetic Foces in Moing Refeence Fames ns F 1 e æ ç1 - è 4pe c ö ø 15 ns Who will see potons hit floo and ceiling fist? 1 4pe Time must un slowe in moing fame. instein 195: On the electodynamics of moing bodies F e Twin paadox +e 1 +e F 1,m B 1 1 F 1,e 5

26 Ou detailed deiations ae not coect fo elatiistic speeds, Accoding to the theoy of elatiity: ( ) ( ) ' ' ' / 1 / 1 c B c B y z z z y y x x ' ' ' / 1 / 1 c c B B c c B B B B y z z z y y x x - ø ö ç è æ - - ø ö ç è æ + Relatiistic Field Tansfomations 6

27 Magnetic Field of a Moing Paticle Still: Moing: B ' z 1 q B 4pe æ ö ç Bz - y - y c è ø c 1- / c 1- / c ' 1 q Slow case: <<c B z - c 4pe 1 c me ' m q B z - Field tansfomation is consistent 4p with Biot-Saat law lectic and magnetic fields ae inteelated Magnetic fields ae elatiistic consequence of electic fields 7

28 ( ) ( ) ' ' ' / 1 / 1 c B c B y z z z y y x x ' ' / 1 / 1 c c z z y y - - lectic Field of a Rapidly Moing Paticle 8

29 Intepetation depends on efeence fame q q F m F e B B lab,, -B ( ) ( ) y - Bz z + By ' ' ' x x y z 1 - / c 1 - / c ' - Bz y» B if << 1- / c c 9