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Magnetic fields/basics

  1. Nov 2, 2005 #1
    I just need to know what I am doing wrong. Maybe there is a concept I don't get right. Please help.

    Find the magnitude and direction of the magnetic field [tex]\vec{B}[/tex] at point P in Fig. 30-32, for i = 30 A and a = 8.0 cm.

    FIG ATTACHED

    My work:

    I see that on the inner side, the magnetic field of all parts is "into." So the problem is finding the individual magnitudes and summing 'em up. Here is what I have

    General procedure for finite wires:

    [tex]B=\frac{\mu _0 I}{4\pi y} \frac{L}{\sqrt{x^2 + y^2}}[/tex]

    Sections
    A:
    [tex]y=\frac{a}{4}[/tex]

    [tex]x=\frac{a}{4}[/tex]

    [tex]L=x[/tex]

    DIR: [tex]\otimes[/tex]

    B:

    [tex]y=\frac{a}{4}[/tex]

    [tex]x=\frac{a}{4}[/tex]

    [tex]L=x[/tex]

    DIR: [tex]\otimes[/tex]

    C:

    [tex]y=\frac{a}{4}[/tex]

    [tex]x=\frac{3a}{4}[/tex]

    [tex]L=x[/tex]

    DIR: [tex]\otimes[/tex]

    D:

    [tex]y=\frac{3a}{4}[/tex]

    [tex]x=\frac{a}{4}[/tex]

    [tex]L=x[/tex]

    DIR: [tex]\otimes[/tex]

    E:

    [tex]y=\frac{3a}{4}[/tex]

    [tex]x=\frac{a}{4}[/tex]

    [tex]L=x[/tex]

    DIR: [tex]\otimes[/tex]

    F:

    [tex]y=\frac{3a}{4}[/tex]

    [tex]x=\frac{3a}{4}[/tex]

    [tex]L=x[/tex]

    DIR: [tex]\otimes[/tex]

    G:

    [tex]y=\frac{a}{4}[/tex]

    [tex]x=\frac{a}{4}[/tex]

    [tex]L=x[/tex]

    DIR: [tex]\otimes[/tex]

    Then, the final result is the following sum

    [tex]B=\frac{\mu_0 I \left( 4\sqrt{5} + 7 \right) \sqrt{2}}{6a\pi} \approx 5.6372 \times 10^{-4} \mbox{ T}[/tex]

    DIR: [tex]\otimes[/tex]

    But, it's wrong!! I can't see why.

    Problem #2.

    Each of the eight conductors in Fig. 30-41 carries 3.4 A of current into or out of the page. Two paths are indicated for the line integral [tex]\oint \vec{B} \cdot d\vec{s}[/tex].

    FIG ATTACHED

    What is the value of the integral for the path at the left?

    My work:

    [tex]\oint \vec{B} \cdot d\vec{s} = \mu _o I_{enc} = \mu _o \left( I + I -I \right) = \mu _o I \approx 4.273 \times 10 ^{-6} \mbox{ T}\cdot \mbox{m}[/tex]

    ANY HELP IS HIGHLY APPRECIATED
     

    Attached Files:

    Last edited: Nov 2, 2005
  2. jcsd
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