HELP urgently physics question

Discussion in 'Physics' started by the_coolest_, Mar 31, 2005.

  1. the_coolest_

    Thread Starter New Member

    Mar 31, 2005
    3
    0
    The wave eqn for a prticle in non conducting or free soace is given by Laplacian(E)=u*e*partial double derivative of (E) with respect to time
    where E is the electric field
    u,e are the permiability and permitivity of free space.

    Now my question is laplacian(X)=Divergence(Gradient of X)
    now X is a scalar Quantity here how can we take gradient of Electric Field E which is a vector quantity??

    my email
    the_coolest_@rediffmail.com
     
  2. Brandon

    Senior Member

    Dec 14, 2004
    306
    0
    Forget about vectors for a moment and go back to calc. The gradient is just a set of derivitives in the end. One in the x, one in the y and one in the z.

    If you take the derivatve of a scalar function, you get a scalar derivative.
    4x+6y-8z=0
    4(dx/dt)+6(dy/dt)-8(dz/dt)=0

    If you take the derivatve of a vector function, you get a vector derivative.
    4x i + 6y j - 8z k=0
    4(dx/dt) i +6(dy/dt) j - 8(dz/dt) k=0

    A derivative or an integral doesn't not change the scalar or vector function type, it only operates on the coefficients and the varibiles. Not the direction.
     
  3. the_coolest_

    Thread Starter New Member

    Mar 31, 2005
    3
    0

    my qs is tht gradient always operates on a scalar quantity and produces a vector quantity. the direction is decided by the maximum rate of change of tht scalar quantity.

    now a vector already has a direction. how can i find the maximum rate of change of a vector???

    if X is a scalar then in cartesian coordinate system then its gradient is given by
    d(X)/dx i +d(X)/dy j +d(X)/dz k
    where d/dx,d/dy,d/dz are the partial derivatives wrt x,y,z
     
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