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!

Electromagnetism electric fields

  1. Dec 31, 2013 #1
    An Electric field has the following form in free space;

    E=Re{Eo exp[j(ωt-κy)[itex]\hat{i}[/itex]

    I am confused as to why a unit i vector is in the expression for an electric field oscillating in the Y direction? and also what does the Re mean ? i was reading somewhere about it being to do with rectangular coordinates.
  2. jcsd
  3. Dec 31, 2013 #2


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    Re is the real part of a complex expression, and [itex]\mathrm{j}[/itex] is used by electrical engineers as the imaginary unit, i.e., [itex]\mathrm{j}^2=-1[/itex].

    A electromagnetic wave in free space must be transverse (both, the electric and magnetic components of the electromagnetic field are vectors perpendicular to the direction of the wave propagation). So what you have here is a plane wave
    [tex]\vec{E}(t,\vec{x})=\left [\mathrm{Re} \; E_0 \cos(\omega t-k y)-\mathrm{Im} \; E_0 \sin(\omega t-k y) \right ] \vec{i}.[/tex]
    This is a wave propagating in [itex]y[/itex] direction (if [itex]k>0[/itex]) and oscillating in [itex]x[/itex] direction).

    That the wave must be transverse follows from Maxwell's equations for free fields in vacuo. Among them you have
    [tex]\vec{\nabla} \cdot \vec{E}=0,[/tex]
    and this is fulfilled for the above wave.
  4. Dec 31, 2013 #3
    Hi Vanhees71 thank you for the swift reply.
    Did you use the Euler relationships to turn the exponential into the sine and cosine functions? i.e [e^jx=cosx+jsinx] and hence the imaginary part can be ignored? or can the expression be left in the exponential form.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook