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Homework Help: Magnetic field created by a solenoid

  1. May 2, 2013 #1
    The problem statement, all variables and given/known data

    Inside a very long, straight and hollow plastic tube (R << L) we have ionized liquid moving at a velocity v = 100 m/s. The net charge per unit volume is n = 106 electrons/m3. The radius of the tube is R = 10cm. Around the tube we have a solenoid, with n = 100 loops/m, through which circulates a current I = 2 A.

    Estimate the magnetic field on the axis of the tube at a distance d >> L.

    Book's answer

    0 T or, considering the system as a dipole, [tex]B=\dfrac{\mu_0}{2\pi d^3}N\pi r^2[/tex]

    My question

    I understand how the magnetic field is 0 T but, how can I consider the system as a dipole to obtain the other answer?

    Thanks in advance!
    Last edited: May 2, 2013
  2. jcsd
  3. May 4, 2013 #2

    rude man

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    Homework Helper
    Gold Member

    Well, we can all see B = 0. But their other answer (dipole) makes no sense since neither the ion nor the wire current I is included in their formula. Probably a typo, but ...

    I would say:
    Consider all the turns of the coil bunched together to form a single-turn loop with current = nLI. That makes using Biot-Savart easy along the axis & is justifiable by d >> L.

    As for the ionic current, about all I could see is trying to compute the magnetic vector potential integral A, then B = del x A.
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