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Homework Help: Different diameter solenoid

  1. Jan 6, 2013 #1
    1. The problem statement, all variables and given/known data

    We're given two solenoids with identical currents and turns per unit length. But the solenoids have different diameters. Would a metal BB experience a larger acceleration in the smaller diameter tube, assuming we use the same BB in both solenoids it accelerates along the z-axis, which goes through the center of the solenoid?

    2. Relevant equations

    Magnetic field through a solenoid:

    [itex] B = \mu_0NI [/itex]

    Where N is number of turns per unit length and I is the current.

    Biot-Savart Law:

    [tex]B = \frac{1}{4\pi}\frac{I\Delta \vec{s} \times \vec{r}}{r^2}[/tex]

    3. The attempt at a solution

    My thought is that since the BB experiences the same uniform magnetic field in both solenoids, the acceleration is the same. The equation for the magnetic field through a solenoid does not include diameter, I notice. But I was having a little debate on this subject and my friend says he would expect the field to sort of dissipate as the diameter increases. This would make total sense if it were a point charge; you'd use Biot-Savart's law. Who is right?
  2. jcsd
  3. Jan 6, 2013 #2


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    hi joe_cool2! :smile:

    (what's a BB ? :confused:)
    you are correct …

    if the solenoid is infinitely long, the magnetic field is uniform

    if the solenoid is ordinary long (ie, a lot longer than wide), the magnetic field is nearly uniform, and you can assume this to be so in exam questions! :wink:

    from hyperphysics

    "The magnetic field is concentrated into a nearly uniform field in the centre of a long solenoid"​
  4. Jan 6, 2013 #3


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    See here for description of BBs. They are often made of steel with a copper or zinc coating, lead, or plastic. I don't see how a BB in a B field (pun intended, sorry) would experience any noticeable acceleration.
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