#### [SOLVED] Electromagnetic Fields of light waves

I'm having trouble visualizing the electric and magnetic field lines of a linearly polarized light/radio wave in 3 dimensional space. When I look at the literature, I get the picture below which seems consistent with the Wikipedia image below. But someone is telling me my picture has the magnetic lines drawn incorrectly. What am I not getting?

I'm not advanced enough to figure it out from the Maxwell's equations on my own. Please include you reference.

#### @Steven Thomas Hatton 2018-01-24 20:23:46

\$2^{nd}\$ Edit: Be aware that the image you borrowed from wikipedia depicts the near-field radiation. The radiation pattern farther than a few wavelengths is, in general, simpler because the "Coulombic" terms fall off as the square of the distance from the source. But the equation I posted below from Feynman, having those terms is for a "naked" charge. Not for a neutral oscillator.

I think the most important aspects of the graphic (which seems basically correct) is the part I originally had wrong. That is, the magnetic portion of the wave wraps around the oscillator. And also that the wave spreads out (almost) spherically, and falls off as the magnitude of the angle from the plane of symmetry increases.

If you are primarily interested in EM radiation in free-space, far from the source, that graphic and associated discussion may be misleading.

Is this wikipedia depiction of near-field radiation accurate?

The reason I am equivocating on the issue of the vanishing of the Coulombic terms is because I'm not sure how relativistic considerations might influence those values.

Edit: My answer was wrong. The magnetic field lines should wrap around the oscillator. The electric field lines should not be loops at all. They point up and down as they spread outward.

I'm not certain the graphic you borrowed is exactly accurate. It shows the electric field line pointing radially from the oscillator at times. I don't believe the radiation equation I am familiar with supports that aspect of the depiction,

http://www.feynmanlectures.caltech.edu/I_28.html#mjx-eqn-EqI283

The only radial components are Coulombic, and therefore will be absent in the case of a neutral oscillator.

But I was wrong once, so it could happen again. I suggest looking at

The Mechanical Universe

Do NOT skip ahead to this time stamp!

One way to think about this is that the radiator causes the neighboring electric field to oscillate in the plane normal to position vector drawn from the (center of the) oscillator to the field point. The resulting electric field lines also lie in the plane spanned by the position vector and the axle of the radiator.

See figures 28-2 and 29-1 in Volume I of The Feynman Lectures on Physics

A changing electric field induces a magnetic field, and a changing magnetic field induces an electric field. So they "leap-frog" through space.

If the radiation is sinusoidal, the fastest rate of change in the electric field will be as it transitions between plus and minus. That is when the magnetic field will be strongest, and changing most slowly. The fastest rate of change of the magnetic field will occur when it transitions from plus to minus. That's when the electric field will be strongest.

The fields are at right angles to one-another.

Unfortunately, Feynman doesn't get into the details until the second volume, at which point he has provided extensive background material.

#### @student509 2018-01-25 00:54:06

I should clarify that my drawing is a part of the wave that is away from the oscillator. My field likes are going around the electric lines.