Electric monopoles cannot radiate?

[Aziza]

According to a physics gre book (Conquering Physics GRE by Kahn &Anderson), electric 'monopoles do not radiate'. They give the example that a uniformly charged sphere can change radius and not radiate...I understand this, but what about just a point charge? Surely it can radiate when accelerated(for example, synchrotron radiation). Should they instead have said that "some" monopoles cannot radiate? Does this mean that "all" accelerating electric dipoles radiate? Any help in understanding this is appreciated! :)

 

[jasonRF]

I am hoping that what the book meant, is that there is no electromagnetic radiator (antenna) that is truly omnidirectional. The uniformly charged sphere that changes radius does not radiate - true - but this is not really a proof of non-omnidirectional EM radiation. I don't believe I have ever seen a proof, but it must have something to do with the ability of producing time changing current density $\mathbf{J}$ that is spherically symmetric; the vector field nature causes the problem here (scalar waves like pressure waves in acoustics can be omni). I have been told (by a TA in an applied math course I took eons ago) that constructing the current density of an omni radiator is essentially the same as trying to comb hair on a sphere without having parts anywhere, and there is apparently a theorem about vector fields that shows it is impossible. I hope that helped.

jason

 

[Aziza]

I am hoping that what the book meant, is that there is no electromagnetic radiator (antenna) that is truly omnidirectional. The uniformly charged sphere that changes radius does not radiate - true - but this is not really a proof of non-omnidirectional EM radiation. I don't believe I have ever seen a proof, but it must have something to do with the ability of producing time changing current density $\mathbf{J}$ that is spherically symmetric; the vector field nature causes the problem here (scalar waves like pressure waves in acoustics can be omni). I have been told (by a TA in an applied math course I took eons ago) that constructing the current density of an omni radiator is essentially the same as trying to comb hair on a sphere without having parts anywhere, and there is apparently a theorem about vector fields that shows it is impossible. I hope that helped.

jason

Thanks for the reply, but my feeling is that this is not what was meant by this book. According to http://en.wikipedia.org/wiki/Monopole_antenna

there do exist monopole antennas, and both monopole and dipole antennas radiate omnidirectionally. Maybe it is not truly omnidirectional, but my guess is that for purposes of the physics gre, this approximation can be taken as valid.

Maybe I should print out the whole statement made by the book:
"By the way, the reason we deal with dipole radiation rather than monopole radiation...is the curious fact that monopoles do not radiate."

Since it is such a strong statement I feel it cannot possibly have been made in error..

 

[Dale]

According to a physics gre book (Conquering Physics GRE by Kahn &Anderson), electric 'monopoles do not radiate'. They give the example that a uniformly charged sphere can change radius and not radiate...I understand this, but what about just a point charge? Surely it can radiate when accelerated(for example, synchrotron radiation).

Monopole radiation is spherically symmetric. It can only happen by spherically symmetric charge distributions and motion.

If you take a point charge and accelerate it then it is not monopole radiation, it is at least dipole radiation, or even higher order spherical harmonics.

 

[vanhees71]

Look for "multipole expansion" in any good E&M textbook (like Jackson).

 

[cmos]

Just to elaborate on the last two posters, what your GRE guide is talking about is multipole moments. An accelerated charge actually acquires a dipole moment (maybe even higher-order moments depending on its motion), and hence radiates. I haven't looked at the problem in some time, but I could imagine a sphere changing radius to not acquire higher-order moments due to its symmetry (i.e. a sphere exhibits continuous rotational symmetry, any other polygon would have a discrete symmetry at best).

Since you brought up monopole antennas: this is just the sloppiness of the engineer. A half-wavelength dipole antenna is the bread and butter of antennas. Interestingly, you can chop this antenna in half (i.e. make it quarter-wavelength long) and stick a "thick" ground plane underneath it. Due to image charges, this new antenna radiates just like like its half-wavelength cousin. This is what is termed a "monopole" antenna. In reality, it's just a fancy way of making a dipole antenna. Note that it actually had nothing to do with monopoles.

 

[sophiecentaur]

I have also heard the term 'unipole' used for a single conductor, perpendicular to a ground plane. That would avoid the confusion.

 

[Dale]

I haven't heard that term, but I agree that it is far better than monopole for that type of antenna.

 

[davenn]

I haven't heard that term, but I agree that it is far better than monopole for that type of antenna.

monopole is the standard RF term tho for that type of antenna and for most of us in that field we know exactly what is being referred to. in 99% of cases a dipole is a 1/2 wave a monopole is a 1/4 wave

Dave

 

[sophiecentaur]

monopole is the standard RF term tho for that type of antenna and for most of us in that field we know exactly what is being referred to. in 99% of cases a dipole is a 1/2 wave a monopole is a 1/4 wave

Dave

So well established, by the Engineers, I think, that the Physicists just have to 'get over it'. The contexts are so different that there would never be any confusion.