1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

(Electric) Scalar and vector potential

  1. Aug 24, 2012 #1
    1. The problem statement, all variables and given/known data

    In the problem, the electric scalar and vector potentials are,
    [itex]\phi=0, \vec{A}=A_0 e^{i(k_1 x-2k_2y-wt)}\vec{u_y}[/itex]

    I have to find E, B and S.

    Then, I have to calculate [itex]\phi '[/itex] that satisfies [itex]div\vec{A}+\frac{\partial \phi '}{\partial t}=0[/itex] Then calculate E and B.

    Is it possible to find [itex]\vec{A}'[/itex] and [itex]\phi'[/itex] that satisfy the previous equation and produce the same E and B as [itex]\vec{A}[/itex] and [itex]\phi[/itex]?

    2. Relevant equations
    [itex]\vec{E}=-grad\phi-\frac{\partial \vec{A}}{c\partial t}=0[/itex]
    [itex]\vec{B}=rot(\vec{A})[/itex]


    3. The attempt at a solution

    Using the equations I find:

    [itex]\vec{E}=A_0wi/c e^{i(k_1x-2k_2y-wt)}\vec{u_y}[/itex]

    [itex]\vec{B}=A_0ik_1 e^{i(k_1x-2k_2y-wt)}\vec{u_k}[/itex]

    [itex]\vec{S}=\frac{c}{4\pi} \vec{E}x\vec{B}=1/(4\pi) A_0^2wk_1sin^2(k_1x-2k_2y-wt)\vec{u_x}[/itex]

    For the next part I find,

    [itex]\phi ' = - 2K_2 c A_0/(w) e^{i(k_1x-2k_2y-wt)}+ constant(x,y)[/itex]

    Then, I calculate E and B as before.

    I don't know how to answer the last part. Any idea?

    Thank you.
     
    Last edited: Aug 25, 2012
  2. jcsd
  3. Aug 24, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Your expression for the vector potential isn't a vector.

     
  4. Aug 24, 2012 #3
    Presumably [itex]A_0[/itex] is itself a vector, which makes that definition perfectly valid.

    Imagine taking your current definitions for [itex]A[/itex] and [itex]\phi[/itex] (I'm renaming your [itex]\phi'[/itex] to [itex]\phi[/itex] for simplicity, and so that I can reuse the symbol [itex]\phi'[/itex] below), and adding new quantities to them. So something like:
    [tex]A \rightarrow A + A'\\
    \phi \rightarrow \phi + \phi'[/tex]

    Now plug those definitions into your previous equations, and see if you can use them to come up with some constraints on the forms that [itex]A'[/itex] and [itex]\phi'[/itex] would have to take, in order to cause [itex]E[/itex] and [itex]B[/itex] to still come out the same.
     
    Last edited: Aug 24, 2012
  5. Aug 24, 2012 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    I don't think so. A0 appears in the expressions for the electric and magnetic fields along with unit vectors. It's pretty clear that the OP meant for A0 to denote a scalar.
     
    Last edited: Aug 24, 2012
  6. Aug 24, 2012 #5
    Hmm, you're right. Guess I didn't look close enough at those E/B solutions.

    lailola, can you clarify what the original problem is, and how you came up with your definitions for E and B?
     
  7. Aug 25, 2012 #6
    I forgot to write the vector in the expression of the vector potential. I've written it.
     
  8. Aug 25, 2012 #7
    Ok, thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook