Magnetism: a new force!


 Clifton Bryant
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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 Efield kq Efields ae ceated by chages: E = 2 Efield 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 Efield foce) The diection of the foce F is pependicula to the plane fomed by and. Diection of F is detemined by the "Righthand 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 = 104 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 Efields, cuents make fields). The field poduced by a long staight wie, caying cuent, has magnitude µ 0 = = distance fom wie, µ o = constant = 4π 107 ( 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 "Righthand 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 Efield lines in this way: Efield 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 massspectomete, 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 Efield, 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 cuentcaying wie A field exets a foce on a moing chage. A cuentcaying wie is full of moing chages, so a field exets a foce on the cuentcaying 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 Cuentcaying 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, Antipaallel 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 cosssection 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 antipaallel cuent epel. opposite poles attact : like poles epel : paallel cuents on ends attact antipaallel cuents on ends epel Dubson Phys2020 otes, Uniesity of Coloado
8 8 Dubson Phys2020 otes, Uniesity of Coloado
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