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!

Derivation of electromagnetic waves

  1. Apr 10, 2015 #1
    I've seen derivations for c=E/B and c=1/√μ0ε0, but I don't seem to get the directions right. i.e. I end up with a negative sign in one of the equations. The derivations I've seen do not use vector calculus.
    One derivation I've seen is in this video. But in this video I don't know how the direction of integration is determined, as that would solve my problem; it seems to contradict Lenz's law. Any help would be grateful!
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Apr 10, 2015 #2

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Can you show some work... so we know which equation has the negative sign?
    Do you know what the "curl" is?
     
  4. Apr 10, 2015 #3
    http://imgur.com/KzXQADm
    Here's my poor limited understanding of em waves without using vector calculus (I've heard of "curl" or "divergence", but don't really know what they are). So my question is that two rectangles have different directions of integration. For example, for the top graph, magnetic field is increasing at the instance the rectangle is taken, so according to Faraday's law, shouldn't the direction of integration be reversed, as the net electric field needs to generate a magnetic field that opposes the change? Or maybe this is just an obvious mistake...
     
  5. Apr 10, 2015 #4

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The integration loops are chosen so that
    the normal to the upper loop (for ##E_y##) points along ##\hat x \times \hat y=\hat z##
    and
    the normal to the lower loop (for ##B_z##) points along ##\hat z \times \hat x=\hat y##

    The circulation of ##\vec E## is positive.... with your right-hand, the electric field curls* counter-clockwise (with its normal along ##\hat z##), which follows the sense of the integration loop. By Faraday, with its minus-sign, that is ##-\frac{\partial B_z}{\partial t}##.
    *(With your right hand, have your right-hand fingers point along the longer Electric Field vector, then bending to curl around the loop to the shorter Electric Field vector.)

    The circulation of ##\vec B## is negative.... with your right-hand, the magnetic field curls clockwise (with its normal along ##-\hat y##), which is opposite the sense of the integration loop. By Ampere, that is ##\frac{\partial E_y}{\partial t}##.

    So, both Faraday and Ampere say that the fields in that interval ##dx## must decrease in the next instant... which is consistent with the entire waveform advancing along the positive-x axis.
     
  6. Apr 11, 2015 #5
    Oh, I see, the curl is what I was missing. Thanks, that helped a lot.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivation of electromagnetic waves
  1. Electromagnetic waves? (Replies: 4)

  2. Electromagnetic Waves (Replies: 6)

  3. Electromagnetic wave (Replies: 6)

  4. Electromagnetic waves (Replies: 1)

Loading...