Lec16-3VV - Lecture 16-1 Lecture Amperes Law in...

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Lecture 16 Lecture 16 -1 Ampere’s Law in Magnetostatics The path integral of the dot product of magnetic field and unit vector along a closed loop, Amperian loop , is proportional to the net current encircled by the loop, 0 tC CC B dl B dl I μ == ∫∫ ur r ± ±± Choosing a direction of integration. A current is positive if it flows along the RHR normal direction of the Amperian loop, as defined by the direction of integration. Biot-Savart’s Law can be used to derive another relation: Ampere’s Law 01 2 () ii
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Lecture 16 Lecture 16 -2 Magnetization and “Bound” Current in Matter Ampere : Aligned magnetic moments in magnetized matter arise due to microscopic current loops inside the material. A Bound current Strong externally applied field B app aligns the magnetic moments in matter. Magnetization M V μ = ur uur d M dV ⎛⎞ = ⎜⎟ ⎝⎠ dA d i μ= magnetic moment due to Amperian current di d i d i M Adl Adl dl === current /length Equivalent to a solenoid of nI=M 0 0 m nI BM = = Note cancellations of internal currents from adjacent loops
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Lecture 16 Lecture 16 -3 MAGNETIC MATERIAL TYPES Magnetic materials are placed inside a solenoid with a magnetic field B s . The following kinds of materials change the resultant B inside the solenoid. (Note, the magnetization of ferromagnetic materials SATURATES in a large enough field: for Iron it’s at around 2 Tesla.) A| Stainless steel (paramagnetic) ~ +1% increase B| Iron (ferromagnetic) ~ +10-100 times increase C| Copper (diamagnetic) ~ -10 -4 decrease
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Lecture 16 Lecture 16 -4 Magnetic Susceptibility Magnetic susceptibility Χ m m app m BB χ = u ru r 0 0 m m > < paramagnet diamagnet 0 (1 ) a ap m pp p BM B B μ = =+ + u u r u r Relative permeability K m 0 m app app M B ∝→ = u ur ur () 0 0 app app mm B BK B K ⎛⎞ == ⎜⎟ ⎝⎠ 0 m K permeability saturation
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Lecture 16 Lecture 16 -5 Reading Quiz 1 Three currents I 1 , I 2 , and I 3 are directed perpendicular to the plane of this page as shown. The value of the Ampere’s Law line integral of B dl counterclockwise around the circular path is - μ o 2I 1 What is the magnitude of the currents in I 2 and I 3 ? a. I 2 =0, I 3 can be any value b. I 2 =0, I 3 can only be zero c. I 2 =I 1 , I 3 can be any value d. I 2 =2I 1 , I 3 can be any value e. I 2 =3I 1 , I 3 can be any value I 1 I 3 I 2
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Lecture 16 Lecture 16 -6 Magnetism Exhibited by Materials Diamagnetism: (small) magnetic moment opposite
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This note was uploaded on 04/23/2011 for the course PHYS 241 taught by Professor Wei during the Spring '08 term at Purdue University-West Lafayette.

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Lec16-3VV - Lecture 16-1 Lecture Amperes Law in...

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