Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By HallsofIvy

Math Help - 3x3 Matrix (Lorentz force law)- determinant

  1. #1
    Junior Member froodles01's Avatar
    Joined
    Nov 2011
    From
    Surrey UK
    Posts
    43
    Thanks
    1

    Angry 3x3 Matrix (Lorentz force law)- determinant

    Using the Lorentz force law for my problem, I get the following matrix.

    I ex ey ez I
    I 1 . -1 . 0 I
    I 1 . 0 . -1 I

    I have evaluated the ey term as a -ve ( ey((1X-1)-(0x1)) = ey(-1-0) = -1ey)

    = ex((-1x-1)-(0x0)) + ey((1X-1)-(0x1)) + ez ((1x0)-(-1x1))
    = ex - ey + ez

    Another person evaluates this term as +ve. so could someone point out the obvious mistake I made, please, I can't see it.

    The set problem is
    An electron in a magnetic field B=2.0T(ex-ez) has velocity v=(2.5x107 ms-1 (ex-ey)
    a) calculate magnetic force on electron at that instant
    Now, F = -e 2(2.5x107) (ex-ez)* (ex-ey)

    so
    F = -8x10-12 (ex - ey + ez)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: 3x3 Matrix (Lorentz force law)- determinant

    You have done the cross product incorrectly. The j coefficient is the negative of the minor.
    Thanks from froodles01
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member froodles01's Avatar
    Joined
    Nov 2011
    From
    Surrey UK
    Posts
    43
    Thanks
    1

    Re: 3x3 Matrix (Lorentz force law)- determinant

    AH! . . . . . I WAS missing something after all.
    Ta!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: 3x3 Matrix (Lorentz force law)- determinant

    The cross product of vectors <a, b, c> and <p, q, r> is
    \left|\begin{array}{ccc}i & j & k \\ a & b & c \\ p & q & r\end{array}\right|
    expanding that on the first row it is
    (br- cq)i- (ar- cp)j+ (aq- bp)k.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Determinant of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 3rd 2012, 02:28 PM
  2. [SOLVED] Derivative of a matrix inverse and matrix determinant
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 24th 2011, 08:18 AM
  3. Need help with determinant of 5X5 matrix
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 3rd 2009, 11:20 AM
  4. Lorentz force law
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: September 20th 2009, 01:54 AM
  5. Determinant of a 5 by 5 matrix
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: July 11th 2009, 07:25 PM

Search Tags


/mathhelpforum @mathhelpforum