What Is the Upper Limit for Hertzian Dipole Dimensions?

[smileandbehappy]

Homework Statement

A Hertzian dipole is short compared with the wavelength of the radiation it emits. It describes ’short’ radio antennas and the scattering of electromagnetic radiation by small particles.

(a) Give an upper limit for the length of a Hertzian dipole antenna operating at 300 kHz and for the size of atmospheric particles that can be considered as Hertzian dipole scatterers at 1014 Hz.

Homework Equations

Well it says the dipole is short in comparision the the wavelength it emits... So: L << c/f ? But I'm not sure...

The Attempt at a Solution

At 300Hz - L(upper limit) = 3*10^8/300*10^3 m (this seems obscenely big...)
Where am I going wrong? Thanks

 

[BvU]

Well, if I copy what you typed in and google it, I get

which is big indeed, but probably not what you meant ?

 

[smileandbehappy]

Well, if I copy what you typed in and google it, I get

View attachment 83654

which is big indeed, but probably not what you meant ?

You are correct that is not what I meant... I missed out some brackets. Apologies for that. The calculation should have been: (3*10^8)/(300*10^3) = 1000m

So what am I doing wrong? 1km Hertzian Dipole is not normal in my limited experience.

 

[BvU]

As I expected, not what you meant . But 1 km isn't really obscene.

100 kHz is in the long wave part of the radio spectrum.
Here it says long wave radio is around 1 to 2 km in wavelength.
And here they even talk about 3 kHz !

And I've been able to get by without any experience with Hertzian dipoles (*).
All I remember is TV antennas on the roof were around .5 m for VHF and .3 m for UHF and that's a lot more than 3 kHz.

(*) However, thanks to you I now googled up an enormous amount of yagi, folded dipole etc. etc. know-how in a very short time !

 

[smileandbehappy]

As I expected, not what you meant . But 1 km isn't really obscene.

100 kHz is in the long wave part of the radio spectrum.
Here it says long wave radio is around 1 to 2 km in wavelength.
And here they even talk about 3 kHz !

And I've been able to get by without any experience with Hertzian dipoles .
All I remember is TV antennas on the roof were around .5 m for VHF and .3 m for UHF and that's a lot more than 3 kHz.

Maybe my answer isn't as ridiculous as it seems... Any idea about how I would go about answering the second part? It has to be related to Rayleigh scattering... But apart from that gem of knowledge I have absolutely no idea.

 

[BvU]

Hehe, no idea either. I like the 1014 Hz (as opposed to "around 1000 Hz"). Why that kind of precision ?
The corresponding wavelength is like 300 km.

Perhaps they meant 10¹⁴ Hz ?

(have to run now...) back later, perhaps.

[edit] Managed to google and by now I'm utterly convinced there is no 'perhaps' : they meant 0.1 PHz