28_Lec-15

28_Lec-15 - Physics 241 Lecture 15 Y. E. Kim October 19,...

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Physics 241 Lecture 15 Y. E. Kim October 19, 2010 Chapter 28, Sections 3, 4, 6 October 18, 2010 University Physics, Chapter 25 1
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October 18, 2010 University Physics, Chapter 28 2 ± $PSHUH·V /DZ LV ± Where the integral is carried out around an Amperian loop and i enc is the current enclosed by the loop ± As an example of $PSHUH·V /DZ , consider the five currents shown below ± The currents are perpendicular to the plane shown ± An Amperian loop is represented by the red line 0en c Bd s P ³ ± ² 01 2 3 ii ´ ´ ³ 0 3 4 id r dB S u Biot-Savart Law $PSHUH¾V /DZ ±²³ ± ² 123 e n c ´ ´
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October 18, 2010 University Physics, Chapter 28 3 $PSHUH·V /DZ ±²³ ± This loop encloses i 1 , 2 , and 3 and excludes 4 and 5 ± A direction of integration is shown above along with the resulting magnetic field ± The sign of the contributing currents can be determined using a right hand rule by pointing your fingers along the direction of integration ± Your thumb will indicate the positive direction of the contributing currents ± ² e n c 0en c Bd s P ³ ± ² ± ² d
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October 18, 2010 University Physics, Chapter 28 4 A Magnetic Field inside Long Wire (1) ± Consider a current i flowing out of the page in a wire with a circular cross section of radius R ± This current is uniformly distributed over the cross sectional area of the wire ± To find the magnetic field , we use an Amperian loop with radius r A represented by the red circle ± The magnetic field is tangential to this Amperian loop so ZH FDQ ZULWH WKH OHIW VLGH RI $PSHUH·V /DZ as 2 Bd s B S A ³³ 0en c P ³
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October 18, 2010 University Physics, Chapter 28 5 Magnetic Field inside Long Wire (2) ± 7KH ULJKW KDQG VLGH RI $PSHUH·V /DZ FRQWDLQV WKH HQFORVHG current which can be calculated from the ratio of the area of the Amperian loop to the cross sectional area of the wire ± Equating the left and right sides using $PSHUH·V ODZ we get or and i e n c A loop wir S r A 2 R 2 B 2 A P 0 A 2 2 0 2 () , 2 Br rr AA A §· d ¨¸ ©¹ A 0en c Bd s ³ 0 , 2 A t
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October 18, 2010 University Physics, Chapter 28 6 Magnetic Field inside Long Wire (3) 0 2 () , 2 i Br rr R P S AA A §· d ¨¸ ©¹ 0 , 2 r A t 0en c Bd s ³
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October 18, 2010 University Physics, Chapter 28 7 Magnetic Fields of Solenoids (1) ± Current flowing through a single loop of wire
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28_Lec-15 - Physics 241 Lecture 15 Y. E. Kim October 19,...

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