Results 1 to 2 of 2

Thread: mathematical question from physics

  1. #1
    MHF Contributor
    Nov 2008

    mathematical question from physics

    $\displaystyle \vec{E}=f_1(z-ct)\hat{x}+f_2(z-ct)\hat{y}+0\hat{z}$
    $\displaystyle f_1(u)$ and $\displaystyle f_2(u)$ are functions of "u"
    i have the formula
    $\displaystyle \nabla \times \vec{E}=-\frac{db}{dt } $
    $\displaystyle \nabla\times\vec{E}=|\begin{array}{ccc}\hat{x} & \hat{y} & \hat{z}\\\frac{{d}}{dx} & {\frac{{d}}{dy}} & \frac{{d}}{dz}|=\\f_{1}(z-ct) & f_{2}(z-ct) & 0\end{array}\hat{-x}\frac{{df_{2}}}{dz}-\hat{y}\frac{{df_{1}}}{dz}+\hat{z0}=-\frac{{d\overrightarrow{B}}}{dt}$

    i want to find B
    so i need to integrate the left side by t
    in order to get B
    but f_1 f_2 are function of u
    how to make a result

    and then i need to show that $\displaystyle B\bullet E=0$
    i cant get 0
    Last edited by Ackbeet; Jun 10th 2011 at 02:14 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Jun 2010
    CT, USA
    Hmm. I get a slightly different cross product from you:

    $\displaystyle \nabla\times\mathbf{E}=\left|\begin{matrix}\hat{x} &\hat{y} &\hat{z}\\ \frac{\partial}{\partial x} &\frac{\partial}{\partial y} &\frac{\partial}{\partial z}\\ f_{1}(z-ct) &f_{2}(z-ct) &0\end{matrix}\right|$

    $\displaystyle =\hat{x}\left(-\frac{\partial}{\partial z}\,f_{2}(z-ct)\right)-\hat{y}\left(-\frac{\partial}{\partial z}\,f_{1}(z-ct)\right)+\hat{z}(0)$

    $\displaystyle =-\hat{x}\,\frac{\partial}{\partial z}\,f_{2}(z-ct)+\hat{y}\,\frac{\partial}{\partial z}\,f_{1}(z-ct)=-\hat{x}f_{2}'(z-ct)+\hat{y}f_{1}'(z-ct).$

    Now then, Faraday's Law gives us that

    $\displaystyle -f_{2}'(z-ct)=-\frac{\partial B_{x}}{\partial t},$

    $\displaystyle f_{1}'(z-ct)=-\frac{\partial B_{y}}{\partial t},$ and

    $\displaystyle 0=-\frac{\partial B_{z}}{\partial t}.$

    Just integrate all three of these equations w.r.t. time, and you should be good to go. What do you get?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Got a physics question or interested in physics?
    Posted in the Math Topics Forum
    Replies: 17
    Last Post: Apr 6th 2016, 07:07 AM
  2. Mathematical Induction Question
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Mar 29th 2010, 11:31 AM
  3. mathematical problem in Physics
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Oct 24th 2009, 11:04 AM
  4. Replies: 1
    Last Post: May 22nd 2009, 08:08 AM
  5. yet another Mathematical Induction question
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: Jun 21st 2007, 07:15 PM

Search Tags

/mathhelpforum @mathhelpforum