# Lecture19 - Units of magne-c ﬁeld: Tesla ...

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Unformatted text preview: Units of magne-c ﬁeld: Tesla  1 T = 10000 Gauss  Surface of earth: 0.5×10‐4 T  Bar magnet:   1.5 T  Strong superconduc-ng magnet: 30 T  Biot‐Savart Law  Current  dS r dB µ0 I dS × r ˆ dB = 4π r 2 µ0 = 4π × 10 −7 T i m / A Inﬁnite straight wire example  Z  a  The segment of wire (total length = 6R) is formed into the shape  shown and carries a current I. What is the magnitude of the  resul-ng magne-c ﬁeld at the point P?  a .  b .  c .  d .  e .  The segment of wire (total length = 6R) is formed into the shape  shown and carries a current I. What is the magnitude of the  resul-ng magne-c ﬁeld at the point P?  a.   b.  c.   d.  e.  Ques-on 1: Equal currents of magnitude I travel into the page in  wires M and N. Eight direc-ons are indicated by leYers A  through H.   The direc-on of the magne-c   ﬁeld at point P is  a.  B.  b.  C.  c.  D.  d.  E.  e.  F.  Solenoid  Z  a  µ0 I B= 2 Approximate solenoid as bunch of separate loops  a2 ( a2 + z ) 3 22 Magne-c ﬁeld at the center of the solenoid  L/2  L : length of solenoid  n: coil density (#/m)  a: radius of the coil  Looks like integra-on is required again, but how?  a  dz  Current through each coil: I  Number of coils in dz: ndz  Z  µ0 I dB = n 2 a 2 dz ( µ0 nI B=∫ − L /2 2 a2 + z ) 3 22 a 2 dz L /2 ( a2 + z ) 3 22 ⎡ ⎤ ⎢ ⎥ ⎥ µ0 nIa 2 ⎢ L/2 −L / 2 B= ⎢ 1− 1⎥ 2⎢ L2⎞ 2 L2⎞ 2 ⎥ 2⎛ 2 2⎛ 2 ⎢a ⎜a + ⎟ a ⎜a + ⎟ ⎥ 4⎠ 4⎠⎥ ⎝ ⎢⎝ ⎣ ⎦ Current through each coil: I  Number of coils in dz: ndz  dz  Z  ⎡ ⎤ ⎢ ⎥ ⎥ µ0 nIa 2 ⎢ L/2 −L / 2 B= ⎢ 1− 1⎥ 2⎢ ⎛ 2 L2⎞ 2 ⎛ 2 L2⎞ 2 ⎥ ⎢ a2 ⎜ a + ⎟ a2 ⎜ a + ⎟ ⎥ 4⎠ 4⎠⎥ ⎝ ⎢⎝ ⎣ ⎦ µ0 nIa 2 B= 2 L ⎛ 2 L2⎞ a ⎜a + ⎟ 4⎠ ⎝ 2 If L>>a  µ0 nIa 2 B~ 2 L ⎛L ⎞ a⎜ ⎟ ⎝4 ⎠ 2 2 1 2 = 1 2 µ0 nI L = µ0 nI 2 L/2 What about the ﬁeld at the very end?  dz  B= ∫ L 0 µ0 nI 2 Z  a 2 dz ( a2 + z ⎡ µ0 nIa ⎢ L B= 2 ⎢2 2 ⎢ a a + L2 ⎣ 2 ( If L>>a  ) 1 2 ) 3 22 ⎤ 0 ⎥ − 1⎥ 2 22 aa ⎥ ⎦ () µ0 nIa 2 L B= 2 a 2 (a 2 + L2 )1/ 2 µ0 nIa 2 B~ 2 L 2 () 1 22 aL = µ0 nI L µ0 nI = 2L 2 µ0 nI B  Ampere’s Law  Amperian Loop  Current  B ⋅ dS = µ0 I ∫ Integral evaluated around any closed path where I is the total current passing through   any surface deﬁned by the path  Example 1: Inside and outside of a wire  Example 2: Solenoid  d  Magne-c Flux  Φ B = ∫ B ⋅ dA From last Thursday: Torque on current loop in magne-c ﬁeld  µ = IA µ : magne-c moment  Magne-c ﬁeld applies torque on magne-c moment  Example: Torque on magne-c moment  B µ Clicker ques-on #3: Which way will the magne-c ﬁeld try to orient the moment?  a.  b.  c.  d.  Clockwise  Counter clockwise  Out of the board  Into the board  ...
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## This note was uploaded on 07/16/2011 for the course PHY 2049 taught by Professor Saha during the Fall '08 term at University of Central Florida.

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