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Current on a spring to withstand a weight.

  1. Apr 6, 2015 #1

    pitbull

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    1. The problem statement, all variables and given/known data
    You have a spring of lenght l, radius R, with N loops and n loops per unit length. If you consider it a solenoid, what current do you need to apply to withstand a mass m hanging from it, without stretching or shrinking the spring.

    2. Relevant equations
    Magnetic field inside a solenoid: B0nIz
    Magnetic energy: W=∫∫∫B2/(2μ0)dV

    3. The attempt at a solution
    I calculated the magnetic energy of a solenoid and I got:
    W=μ0N2I2πR2/(2l)

    The force applied by the mass is:
    F=mg

    So, the magnetic force that I need is:
    F=∇W(length constant)=μ0N2IπR2/(l)

    Both forces must be equal. I solve for I and I get:
    I=mgl/(μ0N2πR2)

    Do you thing it is right?
     
    Last edited: Apr 6, 2015
  2. jcsd
  3. Apr 6, 2015 #2

    mfb

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    The approach looks good, but I get confused by the notation with I, l and l.
    The derivative has to be with respect to length.
     
  4. Apr 6, 2015 #3

    pitbull

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    So should I derivate with respect to length and then equal that derivative to mg?
     
  5. Apr 6, 2015 #4

    mfb

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    Sure. You are interested in the total energy after a length change to see if this length change happens.
     
  6. Apr 6, 2015 #5

    pitbull

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    And after equaling both quantities, I solve for I (current), right?
     
  7. Apr 6, 2015 #6

    mfb

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    Staff: Mentor

    Sure.
     
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