Magnetism: a new force!

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1 -1 Magnetism: a new foce! o fa, we'e leaned about two foces: gaity and the electic field foce. F E = E, FE = E Definition of E-field kq E-fields ae ceated by chages: E = 2 E-field exets a foce on othe chages: F = E. The gaitational foce is simila: GM Gaitational fields ae cea ted by mass: g =. 2 E E The gaitational field exets a foce on othe masses. F = mg. ga Thee is a diffeent kind of field, called a magnetic field o -field. -fields ae ceated by moing chages (cuents). -fields exet foces on moing chages. The foce F fom a -field on a moing chage depends on the elocity of the chage in a peculia way: a chage, moing with elocity in a magnetic field, feels a foce of magnitude F = F = sinθ = θ θ = sinθ f, then sinθ = 1 F = f then sinθ = 0 F f = 0, then F = 0 (unlike gaity o E-field foce) The diection of the foce F is pependicula to the plane fomed by and. Diection of F is detemined by the "Right-hand ule". Use you ight hand. Point you finges in the diection Dubson Phys2020 otes, Uniesity of Coloado

2 -2 of, cul you finges towad. Thumb then points in the diection of F o positie. (Oient hand so that finges cul thu angle < 180 ). f is (-), F if the chage is is othe way F F (out) F (in) F (in) ( ) [F] Units of : [] = [] = = 1 tesla (T) [][ ] = m C s Olde, non-, unit of : 1 gauss = 10-4 T, 1 T = 10 4 gauss Eath's magnetic field 0.5 gauss = 5 10 T kitchen magnet : gauss = T ion coe electomagnet: 2 T (max) (tong en ough to yank tools out of you hand.) supeconducting magnet: 20 T (max) -5 Cuents make -fields You m ake a -field with a cuent. (Chages make E-fields, cuents make -fields). The -field poduced by a long staight wie, caying cuent, has magnitude µ 0 = = distance fom wie, µ o = constant = 4π 10-7 ( units) 2 π (This fomula can be deied fom a fundamental law called Ampee's Law, which elates cuents and -fields.) Dubson Phys2020 otes, Uniesity of Coloado

3 -3 The diection of the -field is pependicula to (out) the diection of the cuent. The -field lines fom cicles aound the cuent, accoding to "Right-hand Rule ": Point thumb of RH along cuent, finges cul along diection of -field. A loop of wie caying a cuent foms a athe complicated -field: -field lines ae fundamentally diffeent fom E-field lines in this way: E-field lines begin and end on chages (o go to ). ut -field lines always fom closed loops with no beginning o end. t is possible to make a unifom, constant -field with a solenoid = cylindical coil of wie: End View: ide View unifom inside Dubson Phys2020 otes, Uniesity of Coloado

4 -4 Motion of a chaged paticle in magnetic field Conside a chage moing in a unifom magnetic field. ince the foce F is always pependicula to the elocity, the foce F does no wok : F WF = 0. The magnetic foce cannot change the KE o PE of the paticle (since Wok done = K E + PE). The -field changes the diection of t he elocity, but does not change the speed. f the elocity is pependicula to the field, the magnetic foce bends the path of the paticle in a cicle. F F F unifom (out) F (out) R We can elate the adius R of the cicula path to the magnitude of the field and the speed with ewton's econd Law: 2 Fnet = m a = m R ( ecall that fo cicula motion a = 2 R ) oling fo R, we get R m =. otice that the adius is popotional to the mass of the paticle. n a mass-spectomete, the mass of an unknown paticle is detemined fom measuement of the adius (chage, speed and -field ae all known). The Velocity electo The elocity selecto is a deice which measues the speed of an ion. (ion = chaged atom with one o moe electons missing). A magnet poduces a unifom -field and a capacito poduces a unifom E-field, with E. Dubson Phys2020 otes, Uniesity of Coloado

5 -5 mass m chage E (in) unifom E down, (in) Foces on chage: F = F E = E The and E fields ae adjusted until the paticle goes staight though. f the path is staight, then F = F E = E = E /. Magnetic foce on a cuent-caying wie A -field exets a foce on a moing chage. A cuent-caying wie is full of moing chages, so a -field exets a foce on the cuent-caying wie. Recall that F = = sinθ. on We will show below that this leads to Fon wie = Lsinθ whee is the cuent, L is the length of the wie, and θ is the angle between the diection of and the diection of th e cuent. (unifom) L F (in) F = L ( diection) Poof of F on wie = L : Conside a section of wie, length L, caying moing chages. moing chages L Assume wie. speed of moing chages = cuent = t Fon wie = Fon = = L = L (done) t L t = L t Dubson Phys2020 otes, Uniesity of Coloado

6 -6 Cuent-caying wies exet magnetic foces on each othe. Wie1 ceates a -field µ 0 ( = ). Wie2 feels a foce due to the -field fom wie A ( Fon wie = L). 2π Paallel cuents attact, Anti-paallel cuents epel. (Can you see why? Use Right hand ule.) F F F F Pemanent Magnets Cuents make -fields. o whee's the cuent in a pemanent magnet (like a compass needle)? An atom consists of an electon obiting the nucleus. The electon is a moing chage, foming a tiny cuent loop an "atomic cuent". n most metals, the atomic cuents of diffeent atoms hae andom oientations, so thee is no net cuent, no -field. n feomagnetic mateials (Fe, i, C, some alloys containing these), the atomic cuents can all line up to poduce a lage net cuent. n inteio, atomic cuents cancel: atoms coss-section of magnetized ion ba on im, cuents all in same diection, cuents add net = 0 n a magnetized ion ba, all the atomic cuents ae aligned, esulting in a lage net cuent aound the im of the ba. The cuent ion ba then acts like a solenoid, poducing a unifom - field inside: Dubson Phys2020 otes, Uniesity of Coloado

7 -7 ide View: unifom (out) End View: net atomic cuent on im atomic cuent on im, like solenoid -field comes out of "oth" end -field entes "outh" end Why do pemanent magnets sometimes attact and sometimes epel? ecause paallel cuents attact and anti-paallel cuent epel. opposite poles attact : like poles epel : paallel cuents on ends attact anti-paallel cuents on ends epel Dubson Phys2020 otes, Uniesity of Coloado

8 -8 Dubson Phys2020 otes, Uniesity of Coloado

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