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I Differentiating Biot-Savart Law

  1. Feb 6, 2017 #1
    Hello!

    I have the equation FM = qvBsinθ .
    As the end result, I am trying to figure out what B I need to change θ even a little bit. To do that, I was planning to find the minimum B by differentiating B=(μe/4π)(qv x R / R3) in terms of R and setting it equal to zero. . I am assuming that this is a form of the Biot Savart Law for things that aren't necessarily wires. Am I on the right track?

    If I am on the right track, let's say I plug in the minimum B value I find into the very first equation. I now have three variables: θ, F, and dR or R. I'm confusing myself here... ignoring the F for now, I am trying to find dθ, if so, any tips on how to get rid of all the variable except for one? (I have q and v and μ as all constants).

    I'm not at all knowledgeable on this topic, but since I'm on a time limit, jumping quite a bit. I'm a high school senior taking Calculus BC, so I can probably figure out the math... I hope :)

    Thank you so much for helping!
     
  2. jcsd
  3. Feb 6, 2017 #2

    mfb

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    2016 Award

    Staff: Mentor

    What do you actually want to do?

    Is this homework?
    What does that mean? θ is the angle between motion and the magnetic field. It depends on the particle flying around. This angle, plus the velocity and the magnetic field, determine the force.

    That formula is at least missing an integral, but I don't think it is really doing what you want. Differentiating it with respect to what, to do what?
     
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