1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Radius and Pitch of an electron's spiral trajectory

  1. Jul 21, 2014 #1
    1. The problem statement, all variables and given/known data
    The uniform 45.6 mT magnetic field in the picture below points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.29E+6 m/s and at an angle of θ = 30.1° above the xy-plane. Find the radius r and the pitch p of the electron's spiral trajectory. (Enter the radius r first and the pitch p second.)
    Picture attached! Please let me know if you cant see it and I'll attempt to try attaching again :D

    B= 45.8mT = 0.0456T
    m= 9.11*10^-32kg

    2. The attempt at a solution
    R=mv/(qBsinΘ) = (9.11*10^-32kg)(5.29*10^6m/s)/[(1.60*10^-19C)( 0.0456T)*sin(90-30.1)]

    For the second part of the question, could someone please explain to me the concept of pitch and possibly how the equation has been derived (d=vsinΘ*2Pi*m/[qB]), because I have searched google and I don't understand it much other than that it is the measurement of the height that the electron has travelled in one revolution~ Or is this equation something I should just memorize?

    Thank you sooo much!
  2. jcsd
  3. Jul 21, 2014 #2
    It's not something you should need to memorize, it's just the distance between points on a helix.

    You should be able to derive the equation you need quite simply if you think a little bit about the components of the electrons velocity.
    If it were travelling in a straight line without any magnetic field you have x- and y-componentnets, then a magnetic field is turned on, how are the components effected?

    The equation you gave:
    isn't completely necessary here you can derive a much simpler equation for it since you already know radius. (hint: or rather, you already know how far the electron will travel in one of its components as it completes a full rotation)

    However, if you're really curious about deriving that equation exactly just be careful with your angles. Remember the one you used was 90-30.1, and not the actual angle shown in the picture.
    The angle used in that equation you found should be the angle shown in the pic.
    Last edited: Jul 21, 2014
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted