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Homework Help: Integrate the on axis field of finite solenoid from a thin shell one, HELP!

  1. Aug 13, 2009 #1
    Dear all,

    i met a problem that i couldn't get the on axis field of a finite solenoid that integrating from a thin shell solenoid equation.

    The thin shell equation link:

    And the on axis finite solenoid equation link:

    If i was right, the integral of (a/sqrt (a*a+r*r)) dr should be a*ln(r+sqrt(r*r+a*a)), if so i couldn't figure out how to get the (r2-r1) term in the second link equation.

    Thank you for your attention

  2. jcsd
  3. Aug 13, 2009 #2


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    Science Advisor
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    Gold Member

    To get the second expression from the first, you need to integrate over dr from r1 to r2. You do this by adding "solenoids" of radius r, thickness dr, and length l carrying current di. According to the first expression, the contribution from one such solenoid is

    [tex]dB = \frac{\mu_{0}N di}{2 l}[\frac{x_{2}}{\sqrt{x^{2}_{2}+r^{2}}}-\frac{x_{1}}{\sqrt{x^{2}_{1}+r^{2}}}] [/tex]

    Before you integrate, you need to express di in terms of dr. Hint: Think in terms of current density.
  4. Aug 13, 2009 #3
    Thank you very much, i got the answer.
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