21.9 Magnetic Materials

Transcription

1 21.9 Magneic Maerials The inrinsic spin and rbial min f elecrns gives rise he magneic prperies f maerials è elecrn spin and rbis ac as iny curren lps. In ferrmagneic maerials grups f neighbring ams frm magneic dmains where he spins f elecrns are naurally aligned wih each her; magneic dmain sizes are ~ mm. An exernal magneic field can induce magneism in ferrmagneic maerials by merging and aligning dmains. Depending n he maerial, he induced magneism may r may n becme permanen. Puing irn in he cener f a slenid can creae a srng elecrmagne wih fields 100x x he applied fields (als, can urn fields n and ff).

2 Chaper 22 Elecrmagneic Inducin

3 22.1 Induced Emf and Induced Curren S far we have deal nly wih currens and magneic fields which are cnsan in ime, and we have shwn ha currens (i.e. mving charges) prduce magneic fields. Can magneic fields prduce currens? --> yes, if he magneic field ging hrugh a lp f wire is changing in ime! There are a number f ways a magneic field can be used generae an elecric curren. I is he changing field ha prduces he curren.

4 22.1 Induced Emf and Induced Curren The curren in he cil is called he induced curren because i is brugh abu by a changing magneic field. Since a surce emf (elecrmive frce) is always needed prduce a curren, he cil behaves as if i were a surce f emf. This emf is knwn as he induced emf.

5 22.1 Induced Emf and Induced Curren An emf can be induced by changing he area f a cil in a cnsan magneic field In each example, bh an emf and a curren are induced because he cil is par f a cmplee circui. If he circui were pen, here wuld be n induced curren, bu here wuld be an induced emf. The phenmena f prducing an induced emf wih he aid f a magneic field is called elecrmagneic inducin.

6 22.2 Minal Emf THE EMF INDUCED IN A MOVING CONDUCTOR dwnward frce n elecrns Each charge wihin he cnducr is mving and experiences a magneic frce F = qvb The separaed charges n he ends f he cnducr give rise an induced emf, called a minal emf.

7 22.2 Minal Emf Derive he minal emf, E, when v, B, and L are muually perpendicular Magneic frce n a charge in he rd F M F M = qvb In equilibrium, he elecric frce f repulsin frm charge buildup a he ends, qe (where E is he elecric field), balances F M qe = qvb è E = vb Gradien equain è E = ΔV/Δs = E/L E/L = vb è E = vbl

8 22.2 Minal Emf Example 1 Operaing a Ligh Bulb wih Minal Emf Suppse he rd is mving wih a speed f 5.0 m/s perpendicular a 0.80-T magneic field. The rd has a lengh f 1.6 m and a negligible elecrical resisance. The rails als have a negligible elecrical resisance. The ligh bulb has a resisance f 96 hms. Find (a) he emf prduced by he rd, (b) he curren induced in he circui, (c ) he elecric pwer delivered he bulb, and (d) he energy used by he bulb in 60.0 s.

9 22.2 Minal Emf (a) E = vbl = ( 5.0m s)( 0.80 T)( 1.6 m) = 6.4 V E (b) I = E R = 6.4 V 96Ω = A (c ) P = IE = (0.067 A)(6.4 V) = 0.43 W (d) Energy = P = (0.43 W)(60.0 s) = 26 J

10 22.2 Minal Emf MOTIONAL EMF AND ELECTRICAL ENERGY In rder keep he rd mving a cnsan velciy, he frce he hand exers n he rd mus balance he magneic frce n he induced curren which acs ppsie he direcin f F hand F hand = F = ILB Using he numbers frm he las example, F hand = (0.067 A)(1.6 m)(0.80 T) = N and he wrk dne by he hand in 60 s is W hand = F hand x = F hand v =(0.086 N)(5 m/s)(60 s) = 26 J = Energy

11 22.2 Minal Emf F The direcin f he curren in his figure gives an induced frce cnsisen wih he cnservain f energy è he direcin f he induced curren ends ppse he applied min -- i deceleraes he rd nce he applied frce is remved (i.e. i akes energy ligh he bulb). The direcin f he curren in his figure wuld prduce a frce which vilaes he principle f cnservain f energy since i acceleraes he rd hus creaing energy u f nhing.

12 22.2 Minal Emf Cncepual Example 3 Cnservain f Energy A cnducing rd is free slide dwn beween w verical cpper racks. There is n kineic fricin beween he rd and he racks. Because he nly frce n he rd is is weigh, i falls wih an accelerain equal he accelerain f graviy. Suppse ha a resisance cnneced beween he ps f he racks. (a) Des he rd nw fall wih he accelerain f graviy? (b) Hw des he principle f cnservain f energy apply?

13 22.3 Magneic Flux RELATIONSHIP BETWEEN MOTIONAL EMF AND MAGNETIC FLUX ( ) ( ) BA BA B A A B L x xl BL x x vbl = " " # $ % % & ' = " " # $ % % & ' = " " # $ % % & ' = = E è magneic flux Φ = BA E In ime 0 an area A 0 is swep u. In ime an area A is swep u. Δ ΔΦ = Φ Φ = E The minal emf equals he change f he magneic flux per ime E

14 22.3 Magneic Flux GENERAL EXPRESSION FOR MAGNETIC FLUX Φ = BAcsφ è depends n he angle a which he B-field crsses he area Unis f magneic flux: T m 2 = Weber = Wb

15 22.3 Magneic Flux Example. A recangular cil f wire is siuaed in a cnsan magneic field whse magniude is 0.50 T. The cil has an area f 2.0 m 2. Deermine he magneic flux fr he hree rienains φ = 0, 60, and 90, as shwn. Φ = BAcsφ φ = 0 Φ = (0.50)(2.0)cs 0 = 1.0 Wb φ = 60 φ = 90 Φ = (0.50)(2.0)cs 60 = 0.50 Wb Φ = (0.50)(2.0)cs 90 = 0 Wb

16 22.3 Magneic Flux GRAPHICAL INTERPRETATION OF MAGNETIC FLUX The magneic flux is prprinal he number f field lines ha pass hrugh a surface.

17 22.4 Faraday s Law f Elecrmagneic Inducin FARADAY S LAW OF ELECTROMAGNETIC INDUCTION The average emf induced in a cil f N lps is E E ) = N ' ( Φ Φ SI Uni f Induced Emf: vl (V) & ΔΦ $ = N % Δ (The minal emf-φ relain we derived is a special case f his.) he minus sign reminds us ha he induced emf will ppse he change in Φ Faraday s law saes ha an emf is generaed if he magneic flux changes fr any reasn. Since Φ = BA cs φ, any change f B, A, r φ will induce an emf.

18 22.4 Faraday s Law f Elecrmagneic Inducin Example 5 The Emf Induced by a Changing Magneic Field A cil f wire cnsiss f 20 urns each f which has an area f m 2. A magneic field is perpendicular he surface. Iniially, he magniude f he magneic field is T and 0.10 s laer, i has increased T. Find he average emf induced in he cil during his ime. ΔΦ BAcsφ B EE = N = N Δ Δ ( B B % = NAcsφ& # = ' Δ $ = V Acsφ ( )( m ) cs( 0) T T 0.10 s