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4 vector problem

  1. Jun 19, 2007 #1
    1. The problem statement, all variables and given/known data

    I cannot remember if I have already posted this question here...
    However,if that is the case,let it be said that I want to discuss more about it.

    Let us define 4 vector by 4 co-ordinates (x1,x2,x3,x4) where (x1,x2,x3) are space components (like x,y,z) and x4 is related to time as x4=ict.Express the following equations in tensor notation.

    (i)The continuity equation: div J+(del*rho/del t)=0

    (ii)The wave equation del2ø-(1/c2) [del2 ø/del t2]=0

    (iii)What will be the value of j4 instead of above?

    2. Relevant equations

    3. The attempt at a solution

    For the first two part I am getting these:

    Please check...

    Let me know if I am correct.


    (i) (∂/∂x_i)(J_i)+ (∂/∂t)ρ=0


    (ii) [∂^2/(∂x_i*∂x_i)]ψ-(1/c^2)[(∂^2/∂t^2)ψ]=0

    I have changed phi to psi...

    Do not mind.

    How can I get the 3rd part?
     
  2. jcsd
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