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!

Electron entering a magnetic field

  1. May 23, 2013 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=58972&stc=1&d=1369329352.jpg


    2. Relevant equations



    3. The attempt at a solution
    At any instant in the circular region, let the horizontal and vertical components of velocity of electron be ##v_x## and ##v_y##. Let the origin be at the point from where the electron enters the magnetic field. Positive x-axis is in horizontal direction to left and positive y-axis in vertically upward direction.

    The force acting on the electron is
    [tex]F=q\vec{v}\times \vec{B}[/tex]
    [tex]F=q(v_x\hat{i}+v_y\hat{j}) \times (B\hat{-k})[/tex]
    [tex]\Rightarrow F=qv_yB\hat{i}+qv_xB\hat{j}[/tex]

    From the above equation, ##dv_x/dt=qv_yB## and ##dv_y/dt=qv_xB##
    As ##v_x^2+v_y^2=v^2##, hence ##v_xdv_x=-v_ydv_y##. If I substitute for ##dv_x## and ##dv_y##, I end up proving ##1=1##. :confused:

    Any help is appreciated. Thanks!
     

    Attached Files:

  2. jcsd
  3. May 23, 2013 #2
    Since you are given the speed of the electron, you can find the radius of curvature of its path (and hence the equation of the circular path). Then you can find the length of the path inside the field and calculate the time taken to travel.
     
  4. May 23, 2013 #3
    Do you want me to set up a coordinate system, make equation for the two circles and calculate the arc length? Wouldn't that be too dirty? :yuck:

    [tex]r'=\frac{mv}{eB}[/tex]
    ##r'## is the radius of curvature for the electron's path.
     
  5. May 23, 2013 #4

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Draw a sketch of the trajectory passing through the B-field region. Mark the center of the circular trajectory. See if you can construct some triangles that will allow you to find the angle (with vertex at the center of the trajectory) subtended by the arc of the trajectory inside the B-field region. You won't need to introduce a coordinate system or solve simultaneous equations.
     
  6. May 23, 2013 #5
    I still have got no idea. :(
    See attachment for the sketch of trajectory.
    (The trajectory won't be a circular path outside the magnetic field.)
     

    Attached Files:

  7. May 23, 2013 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

    You need angle CAB. Construct triangles AOC and AOB.
     
  8. May 23, 2013 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    ... and consider what angle ACO is.
     
  9. May 23, 2013 #8
    That was really obvious. Why I couldn't think of it. :P

    Thank you both, I have got the right answer. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted