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: Finding the curl of B

  1. Apr 24, 2013 #1
    1. The problem statement, all variables and given/known data

    The electric and magnetic fields in a plane wave propagating in free-space in the z-direction can we represented by (in complex-exponential notation)

    E(x, y, z, t) = E_0 e^i(kz−wt+d ) and B(x, y, z, t) = B_0e^i(kz−wt+d )

    Starting with the Ampère-Maxwell law, ∇ x B =μ_0 ε_0 dE/dt , show that E_0 = −c(z×B0).

    2. Relevant equations

    3. The attempt at a solution

    I'm only having problems when I do curl B (differentiating E is no problem). I'm using the matrix method, but by just looking, it seems like it should be zero since B is in the z direction and there's no field in the x or y direction i.e



    0_______0____B_0e^i(kz−wt+d )

    I should be getting something like ike^(...), but I'm not. Any insight would be helpful

    Last edited by a moderator: Apr 24, 2013
  2. jcsd
  3. Apr 24, 2013 #2


    Staff: Mentor

    While B is in the z direction only, the curl B will have components in the x and y directions and not the z direction. So you should review the curl definition again and see where you went astray.
  4. Apr 24, 2013 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    The wave is propagating in the z-direction. The magnetic field doesn't point in the z-direction.
  5. Apr 24, 2013 #4
    Sorry, what I meant was from doing the calculation, I found the answer to be zero. That's what I found confusing. It shouldn't be zero.

    Am I assuming wrong that d/dx and d/dy of B will come out as 0 since it's differentiating constants as there are no x or y variables in the field?

    Basically, this is what I got from doing curl B:

    x_hat[d/dy e^(...) - d/dz (0)] -y_hat[d/dx e^(...) - d/dz(0)] + z_hat[0-0]
    Last edited by a moderator: Apr 24, 2013
  6. Apr 24, 2013 #5
    Ahh, of course, they're supposed to be orthogonal. I was under the impression that the magnetic field was in the z direction.
    Last edited by a moderator: Apr 24, 2013
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted