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!

Homework Help: Rotation of Electric Field

  1. Jan 10, 2014 #1
    1. The problem statement, all variables and given/known data

    Suppose an E-field is rotated by angle ø2. Express ø2 in terms of:


    2. Relevant equations

    3. The attempt at a solution

    I used the rotation matrix, and compared LHS and RHS but it led to nowhere:
    [tex] E'= RE [/tex]
    [tex]\left ( \begin{array}{cc}
    E_1' sin (ky-ωt+ø_2) \\
    0 \\
    E_2' cos (ky-ωt+ø_2)
    \right )


    \left ( \begin{array}{cc}
    cos ø_2 & 0 & sin ø_2 \\
    0 & 1 & 0 \\
    -sin ø_2 & 0 & cos ø_2
    \end {array}

    \left ( \begin{array}{cc}
    E_1 sin (ky-ωt) \\
    0 \\
    E_2 cos (ky-ωt+ø_1)
    \right )[/tex]
  2. jcsd
  3. Jan 10, 2014 #2


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    It's a very badly post question, because it's not defined around which axis you should rotate. I guess it's the [itex]y[/itex] axis from what's in the white box. You should send the complete question or ask those who have posed the problem for clarification ;-)).

    This said, the behavior of the electric field under rotations is very well defined, because [itex]\vec{E}[/itex] is a vector field (in the sense of 3D Euclidean space),
    [tex]\vec{E}'(t,\vec{r}')=\hat{R} \vec{E}(t,\vec{r})=\hat{R} \vec{E}(t,\hat{R}^{-1} \vec{r}').[/tex]
    The emphasis is on field, because you have to consider both the field value and the spatial argument in the transformation rule!
  4. Jan 11, 2014 #3
    Sorry, I don't really get what you mean. Do you mean a matrix multiplication: [tex]\vec{E}'(t,\vec{r}')=\hat{R} \vec{E}(t,\vec{r})[/tex] ?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted