Department of Physics & Astronomy -...
Transcript of Department of Physics & Astronomy -...
![Page 1: Department of Physics & Astronomy - …jhalekas/teaching/physII_2016/...The'figure'below'shows'four'identical'currents'i' and'five'Amperian'paths'encircling'them.'Rank' the'paths'according'to'the'line'integral'of'B'](https://reader033.fdocuments.net/reader033/viewer/2022042400/5f0ea88a7e708231d4404d32/html5/thumbnails/1.jpg)
Professor'Jasper'Halekas'Van'Allen'70'[Clicker'Channel'#18]'MWF'11:30A12:30'Lecture,'Th'12:30A1:30'Discussion''
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! Van'Allen'and'Wert'Summer'Research'Grants'! These'programs'provide'funding'to'work'on'undergraduate'research'with'faculty'members'
! Short'proposals'(with'endorsement'of'faculty'member)'due'to'Heather'in'the'main'office'by'May'2'
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! The'figure'below'shows'four'identical'currents'i'and'five'Amperian'paths'encircling'them.'Rank'the'paths'according'to'the'line'integral'of'B'taken'in'the'directions'shown,'most'positive'first'and'most'negative'last.'
! 1)'all'tie'! 2)'a,'b'='d,'c,'e'! 3)'d,'a'='c'='e,'b'! 4)'d,'a'='e,'b,'c'! 5)'c,'b,'a'='e,'d''
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Solenoid(
A'single'wire'tightly'coiled'up'into'loops.''Since'it'is'a'single'wire,'the'current'magnitude'is'the'same'in'all'parts'of'the'coil.'
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20 ˆ4 r
rLdiBd ×=
πµ
Moving'charges'(currents)'create'BAfields.'
Where(are(the(moving(charges?(
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Atoms'have'Magnetic'Dipole'Moments'from'the'orbit'of'the'electrons.'
Ai
=orbit)(µ
Electrons'themselves'also'have'a'Magnetic'Dipole'Moment.''
spin)or electron (µ
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In'most'materials'all'the'magnetic'moments'have'random'and/or'canceling'orientations.'
Superposition'of'BAfield'vectors'over'many'atoms'gives'B=0'
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Orbital'Magnetic'Moment:'
Spin'Magnetic'Moment:'
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M'='μtotal/V'='magnetic'moment'per'volume'='magnetization'
B'='B0'+'μ0M'='(μ/μ0)B0'='KmB0='total'magnetic'field'in'material'' ' ' '[B0'='externally'applied'field]'
μ'='Kmμ0'='μ0B/B0='magnetic'permeability''[Km'=''relative'permeability]''[Analogous'to'dielectric'permittivity'&'dielectric'constant]'''
Magnetic'susceptibility'χm'='Km'–'1'='μ0M/B0'
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! Intrinsic'magnetic'moments'line'up'opposite'to'applied'field'! Negative'susceptibility'
! No'simple'electrostatic'equivalent''! Diamagnetism'is'very'weak'
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! F'='Gradient'(B"μ)
μ'
https://www.youtube.com/watch?v=A1vyBAO5i6E'
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! Intrinsic'magnetic'moments'of'atoms'line'up'parallel'to'external'magnetic'field'! Positive'susceptibility'(usually'weak)'
! Somewhat'equivalent'to'polarization'of'insulator''! M'='C'Bext/T'
! C'='Curie'constant'! T'='temperature'
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In'Ferromagnetic(materials'(Fe,'Ni,'Cr,'some'alloys'containing'these'metals'too),'the'atomic'magnetic'moments'can'all'orient'the'same'way'(domains),'making'a'net'BAfield.'
B'
B'
B'
B'
Ferromagnetic'materials'can'have'very'large'magnetic'susceptibility'
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Sometimes'the'material'is'fragmented'into'many'domains'(top)'and'is'thus'unmagnetized.'''If'the'domains'align'(bottom)'there''is'a'net'magnetic'field'(magnetized).'This'magnetization'can'remain'after'the'magnetizing'field'is'removed'(unlike'diamagnetism'or'paramagnetism)''