Results 1 to 2 of 2

Thread: A Physical System :particularly hard lol

  1. #1
    Aug 2007

    A Physical System :particularly hard lol

    a really hard one here. would appreciate if you could start me off:

    a physical system is governed by the following:

    curl E = $\displaystyle -\frac{\partial B}{\partial t}$,
    div B = 0,
    curl B = J + $\displaystyle \frac{\partial E}{\partial t}$,
    div E = $\displaystyle \rho$
    where t = time, and time derivatives commute with $\displaystyle \nabla$

    how could you show that $\displaystyle \frac{\partial p}{\partial t}$ + div J = 0
    when $\displaystyle \rho = 0$ and J = 0 everywhere how can you show that:
    $\displaystyle \nabla^2E - \frac{\partial^2E}{\partial t^2}$ = 0
    $\displaystyle \nabla^2B - \frac{\partial^2B}{\partial t^2}$ = 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Rebesques's Avatar
    Jul 2005
    My house.
    Playing around with Maxwell's equations?

    Name the given relations (1)-(4). For the first question, we get from (4) that
    \frac{\partial p}{\partial t}=\frac{\partial (div {\bf E})}{\partial t}=div\frac{\partial {\bf E}}{\partial t}
    $ and substitute J and curlB from (3) to get $\displaystyle
    \frac{\partial p}{\partial t}=div\frac{\partial {\bf E}}{\partial t}=div(curl {\bf B}-{\bf J})=-div{\bf J},
    $ as $\displaystyle divcurl=0$.

    For the second one, the identities $\displaystyle div{\bf B}=0, div{\bf E}=0$ mean the vector fields are solenoidal, so there exist scalar functions $\displaystyle B,E$ such that $\displaystyle {\bf B}=curlB, {\bf E}=curlE$. Use now (1) and (3), remembering that $\displaystyle curl(curl E)=\nabla(divE)-\nabla^2 E$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Physical bonds
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: Jun 10th 2010, 12:20 PM
  2. physical meaning
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Jul 10th 2009, 02:26 AM
  3. Physical Fitness Probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Apr 18th 2009, 10:52 AM
  4. Hard System, please help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Apr 15th 2008, 08:30 AM
  5. Physical work done by force
    Posted in the Advanced Applied Math Forum
    Replies: 5
    Last Post: Jan 22nd 2007, 07:35 PM

Search Tags

/mathhelpforum @mathhelpforum