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Magnetic field from electric field given a function of time

  1. Jan 26, 2015 #1
    1. The problem statement, all variables and given/known data
    An em wave in free space has an electric field vector E = f(t-z/c0)x where x is a unit vector in the x direction and f(t)= exp(-t22)exp(j2πv0t). Describe the physical nature of this wave and determine an expression of the magnetic field vector.

    2. Relevant equations
    Maxwells faradays law ∇XE=-μ δH/δt

    3. The attempt at a solution

    I have two things I´m not so sure about. Given f(t) will the electric field now become
    E= exp(-(t-z/c0)22)exp(j2πv0(t-z/c0))x

    If so, when I use the curl of the field (dEz/dy-dEy/dz)x+(dEx/dz-dEz/dx)y+(dEy/dx-dEx/dy)z
    I assume everything is 0 except for dEx/dz which I´m not sure because it´s multiplied by a unit vector y.
    when I derivate by z I then have to intergrate by on both sides of the max eq. but I get a very complex integral.
    So where I did I get lost.
    Thanks in advance.
    P.S. Describing the physical nature of this wave? Do I need to state that the wave is linaear homogenous and Isotropic.
  2. jcsd
  3. Jan 26, 2015 #2
    Hi. For the physical nature of the wave, you can ask yourself: is it polarized, and if yes in which direction? is it propagating, and if it is in which direction? how is the amplitude: constant or changing?
    For the B field, you can start by determining the charges and currents present. Then you should be able to use Maxwell's equations to determine a simpler relation between E and B...
  4. Jan 26, 2015 #3
    Scratch the second part of my answer, you can actually use ∇ × E = –μ ∂B/∂t directly, as you started:
    the curl is easy to take, then integrating with respect to time becomes easy as well since t and z/c0 enter in the equation in (anti-)symmetric way...
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