Hukum Ampere by elipldoc

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									      FI-1201
      Fisika Dasar IIA


                    Kuliah-10
                  Hukum Ampere


          Physics Study Program
          Faculty of Mathematics and Natural Sciences
PHYSI S   Institut Teknologi Bandung
Ampere’s Law




   Physics Study Program
   Faculty of Mathematics and Natural Sciences
   Institut Teknologi Bandung
            Medan magnetik dari kawat lurus panjang

                                                                                      0 I
                                      gunakan Hk Biot-Savart                       B
                                                                                      2r
r
                  I
    B                       Ambil vektor
                            pendek , ds
                                                                   B  ds  B  ds cos
                  ds
                                 0  cos  1                                B  ds  B ds


    Perkalian skalar antara B &                                           0 I
                                                                 B  ds       ds
    vektor pendek ds adalah:                                              2r
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        PHYSI S
         Jumlah B.ds di sekitar lintasan lingkaran


                                                                0 I
r                                                      B  ds       ds
                  I                                             2r
    B                             Jumlahkan ini untuk seluruh cincin
                  ds                        0 I     0 I
                                 B ds   2r ds  2r  ds
Keliling
lingkaran             ds  2r                       B  ds 
                                                                 0 I
                                                                      2r  0 Ι
                                                                 2r
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        PHYSI S
   Jumlah B.ds di sekitar lintasan lingkaran


     B  ds   Ι
    circ.
                           0       N.B. this does not depend on r


In fact it does not depend on path                    B  ds   Ι
                                                     path
                                                                     0




Ampere’s Law:                B  ds
                            path
                                              on any closed loop      0 Ι


           is the current flowing Teknologi Bandung
   where IPhysics Study Program - FMIPA | Institutthrough the loop
 PHYSI S
   Hukum Ampere

   B  ds   Ι
                                                                   Sign comes from direction
                          0                                        of loop, current & right
  path                                                             hand rule

                                                                        I

 B  ds  2 Ι
path
                         0
                                         B                              I

                                                                            I
    B  ds  0
   path
                                             B
                                                                                I
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 PHYSI S
        Hukum Ampere
                                                                           Sign comes from direction

  B  ds  2 Ι
                                                            I              of loop, current & right
                              0                                            hand rule
 path                                  B                     I

                                                                       I
 B  ds  2 Ι
path
                               0

                                                                    BI

                                                                        I
 B  ds  2 Ι
path
                                0
                 Physics Study Program - FMIPA | Institut Teknologi Bandung
                                                  B                        I
       PHYSI S
    Hukum Ampere
                   B  ds   Ι
                  path
                                               0           B  ds


 No Different Physics from Biot-Savart Law
 Useful in cases where there is a high
  degree of symmetry
 C.f. Coulomb’s Law and Gauss’s Law in
  electrostatics

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PHYSI S
 Quiz
                                                                   Currents of 1A, 5A,
                              a                                    2A, flowing in 3 wires
                                                                   as shown
  1A                             b                                       What is B.ds
                                                       5A                through loops
                                                                         a, b, c, d?


                    c                           2A

                                               B.ds       -10        +30   +40   +60
                                               a
                                               b
                                               c
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PHYSI S                                        d
Examples of using Ampere’s
Law




   Physics Study Program
   Faculty of Mathematics and Natural Sciences
   Institut Teknologi Bandung
    Examples
 Long-straight wire
 Insider a long straight wire
 Toroidal coil
 Solenoid




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PHYSI S
Long Wire




   Physics Study Program
   Faculty of Mathematics and Natural Sciences
   Institut Teknologi Bandung
 Magnetic Field from a long wire

                                            By symmetry                  Br1  Br 2  Br
    r
                        I                    Ampere’s
                                             Law on                      B|| r1 l1  Br l2
                   B||(r1)
                                                                          B|| r2 l1  Br l2  0
                                             Loop 2

                                            Br2
                                                                       B|| r1 l1  B|| r2 l1  0
   Br1           Loop1




                 B||(r1)                                               B|| r1   B|| r2 

                                                            B r   B|| r     0
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                                                                ||
PHYSI S
                   Magnetic Field from a long wire
          r
                         I
                            For any closed
                            Ampere Loop the
                By symmetry radial components
                                                             Br3
                            will always cancel                        Br4
                            out

                Loop 2
Br1                                  Br2                     Loop 3
                                               Br1
       Thus there is no way to balance a
       current by a radial component or                                     Br2
       produce a radial component from a Teknologi Bandung
                Physics Study Program - FMIPA | Institut
       current
      PHYSI S
  Magnetic Field from a long wire
                                        Tangential component

     r
                             Take a circle of radius
                             r as the Ampere Loop
                                                           B  ds   I
                                                          Circle
                                                                      0
                    I
                           Tangential
                           component
                                             B  ds  B ds
             By symmetry at
             constant r
                                                B  constant

             L.H.S.       B  ds  B  ds
                        Circle                Circle
                                                           2rB

                                                          0 I
                       2- B |  Teknologi Bandung
L.H.S. = R.H.S Program rFMIPAInstitutI
         Physics Study                     or          B
                                                          2r
                                    0
 PHYSI S
Di dalam suatu kawat




   Physics Study Program
   Faculty of Mathematics and Natural Sciences
   Institut Teknologi Bandung
  Di dalam suatu kawat berarus I0

         Kita pilih loop Ampere berupa lingkaran dengan jari-jari r

         Asumsikan rapat arus adalah homogen
         sehingga arus yang mengalir dalam loop
         adalah                             a                                  r 2   r2
                                                             I          I0    2 I0  2 I0
                                                                    A          R     R

                                        r            A           Sama seperti sebelumnnya


                                                            0 I
 B  ds  2rB   I                       0            B                   B  0
                                                                                       r
                                                                                     2R
                                                                                          I
                                                            2r
                                                                                         2 0
Circle      Physics Study Program - FMIPA | Institut Teknologi Bandung

PHYSI S
     Medan B dari suatu kawat panjang


                       r
              B  0      I
                     2R 2 0


B
                                                              0 I 0
                                                           B
                                                              2r



                                     R
                             r
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    PHYSI S
Toroidal Coil




   Physics Study Program
   Faculty of Mathematics and Natural Sciences
   Institut Teknologi Bandung
                                                  Toroidal Coil
                               I0
              r                         Toroid has N loops of wire,
                                        carrying a current I0

                                        Ampere Loop,
                                        circle radius r




                                            No current flowing through
                                            loop thus B = 0 inside the
                                            Toroid
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PHYSI S
                                                                 Toroidal Coil

                                                                       Ampere Loop,
                                                         I0            circle radius r
                        r

                                                         For each wire going in there
                                                         is another wire comeing out
                                                         Thus no nett current flowing
                                                         through loop thus B = 0
                                                         outside the Toroid

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PHYSI S
                                                                         Toroidal Coil
                                              I0
              r                                                                Zoom




Toroid has N loops of wire
 Ampere Loop,                                         For each loop of the coil an
 circle radius r                                      extra I0 of current passes
                                                      through the Ampere Loop

     B  ds  2rB                          0 I              0 NI 0  B   0 NI 0
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   Circle
    PHYSI S                                                                     2r
    Medan B di dalam Toroida
   Toroid berbentuk donut dengan dililiti
    koil.

                                                                     ds
     B  ds B2r  0 NI
                                                                        r
   Maka,                       0 NI
                            B
                                2r

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PHYSI S
Solenoid




   Physics Study Program
   Faculty of Mathematics and Natural Sciences
   Institut Teknologi Bandung
    Infinitely Long Solenoid




      Wire carrying a current of I0 wrapped around
      with n coils per unit length

Zoom looks very
similar to the
toroid with a very
          Physics
large radius Study Program - FMIPA | Institut Teknologi Bandung
  PHYSI S
   Infinitely Long Solenoid




     Wire carrying a current of I0 wrapped around
     with n coils per unit length

Field at centre is
same as torus of                                                        B   0 nI 0
infinite radius
           Physics Study Program - FMIPA | Institut Teknologi Bandung

 PHYSI S
    Medan magnet di dalam Solenoida
   Jika solenoida terdiri dari
    jumlah lilitan N dan
    panjang adalah l, maka:


                                                                            l
                                                                     ds
     B  ds Bl  0 NI
            0 NI
     B                     0 nI
                 l
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PHYSI S
    Resume
   Hukum Ampere
       Lebih mudah dipakai dibandingkan Hukum Biot-Savart


        dalam banyak kasus
    Contoh                                     0 I
                                                                        B  ds   Ι
                                                                       path
                                                                                           0

       Kawat panjang                       B
       Dalam kawat                            2r
        Toroida                                                        r
    
                                                              B  0      I
       Solenoida                                                    2R 2 0


                                                    0 NI 0
                                                 B                           B   0 nI
                         B   0 nI                  2r
          Physics Study Program - FMIPA | Institut Teknologi Bandung

PHYSI S

								
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