Re: [Phys-L] transverse waves

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of John
> Denker
> Sent: Tuesday, April 26, 2016 5:57 PM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] transverse waves
>
> On 04/26/2016 01:11 PM, I asked:
>
> > Question:  What's wrong with the following diagram:
> >   http://www.kshitij-iitjee.com/Study/Physics/Part6/Chapter34/70.jpg
> > from
> >
> > http://www.kshitij-iitjee.com/production-of-electromagnetic-waves-by-a
> > n-antenna

I think that diagram is okay.   It has the problem that any 2D slice of an electric field diagram has but one can still make sense of it.  In the plane of the diagram, it shows the spacing between the radial segments of the electric field lines increasing like r, suggesting that the field is dying of like 1/r, whereas the the spacing between the tangential segments does not change with increasing r suggesting that it is not dying off at all.  If we rotate the diagram about the dipole axis, replicating it, say, every 5 degrees, to create a 3D diagram we have the number of radial segments per spherical shell surface area dying off like 1/r^2 whereas the number of tangential segments per area dies off like 1/r.  To me, one spherical surface of it would be very much like your diagram except that one would have no hesitation to have the curve segments on the spherical surface ending at lots of points on the surface so one could use the traditional interpretation of the electric field magnitude being related to the spacing between the lines (measured perpendicular to the lines) as opposed to the thickness of the lines.  One doesn't have to worry about violating the rule that non-looping electric field lines begin and end on charged particles because the curve segments represent only the transverse component of the electric field lines.  With that modification to your drawing convention, the endpoints of the curve segments would correspond to the radial parts of the field lines.  Note that with increasing distance from the source, the number of endpoints remains the same but the area of the spherical surface increases like r^2 meaning that that contribution to the field is dying off like 1/r^2.  The spacing between the curve segments tangent to a sphere centered on the dipole, measured along latitudinal circles, is increasing like the circumference of a latitudinal circle meaning the transverse field is dying off like 1/r.