Radiating Fields & Static fields

[azaharak]

The intensity of radiative fields or radiating fields (from accelerating charges, or AC current in a circuit) falls off with the inverse square dependence.

Electric fields from point charges fall off with inverse square dependence because we have single pole charges.

There are no monopoles or non detected for magnetism, thus the dipole term contributes an inverse cubic dependence.

So why does the EM radiation fall of with inverse square depence.

Obsviously intensity has to fall off with the surface area of a sphere for a symmetrical configuration.

In DC, or static fields, the field is the contribution from many different points, which may have taken different time paths to get there. Since the case is static then they vectorally add the same at any point in time.

In the AC case, now you have to consider where you are anaylizing the time delay or retarded nature from all the sources. Is this where the r squared nature arises from?

Now what if we anaylize the magnetic field of a current carrying ring in the static case. Along the axis the field falls off like ~ R^2*(R^2+x^2)^(-3/2).

This is obsvously a symmetrical point. My question is , (if you were to power this ring with AC), would the magnetic field fall off with the same intensity along the axis.

Now there should be no delay or retarding effect since it is the same distance to any point in the ring?


Or is this forumlar no longer valid?


Thanks in advance

 

[azaharak]

Or here is another version of my question.


IF you mapped out the magnetic field everywhere around this circular loop DC current, would it look exactly the same as if you decided to put AC through it but with a sinusoidal dependence,


or does the field only look the same along the axis beceause of the symmetry. By same i mean DC field with the sinusoidal depence.


Thanks

 

[azaharak]

Am I also correct in saying that frequency plays a role in what the net field will be, the higher the frequency the larger the interference effects from delayed waves reaching a point.

 

[AJ Bentley]

There are no monopoles or non detected for magnetism, thus the dipole term contributes an inverse cubic dependence.

So why does the EM radiation fall of with inverse square depence.

The dipole term is referring to (in this case) a magnetic dipole - a simple bar magnet for example.
Similarly, the electrostatic dipole is referring to two opposite charges in a static configuration and the inverse cube field relates to that static condition.

This is not to be confused with a dipole radiator, which is essentially an oscillating electrostatic dipole.

In the case of EM radiation, something entirely different is happening. The E field close to the dipole is oscillating. A changing E field generates a changing B field and the changing B field generates another changing E field. This little 'bubble' or vortex of swapping fields moves away from the dipole at the speed of light and more 'bubbles' are formed behind it. This, not the static E field of the 'ordinary' dipole, is EM radiation.

 

[azaharak]

Thanks AJ

So then if you look at my previous post about the helmholtz like coil.

A ring of current DC (circular loop) , creates a mag field along the axis that falls of ~ R^2/(R^2+z^2)^(3/2). For large distances away its like ~z^-3



If we apply a AC current instead, wouldn't the magnetic field just be the same with a sinusoidal dependence? And if so, this field still falls off with z cubed far away. Intensity is proportional to B field squared which gives z ^-6 far away??


Here is a link for a lab that kinda illustrates the example I'm talking about

http://sbhepnt.physics.sunysb.edu/~rijssenbeek/PHY134_Induction.html

 

[AJ Bentley]

Thanks AJ

So then if you look at my previous post about the helmholtz like coil.

A ring of current DC (circular loop) , creates a mag field along the axis that falls of ~ R^2/(R^2+z^2)^(3/2). For large distances away its like ~z^-3



If we apply a AC current instead, wouldn't the magnetic field just be the same with a sinusoidal dependence? And if so, this field still falls off with z cubed far away. Intensity is proportional to B field squared which gives z ^-6 far away??


Here is a link for a lab that kinda illustrates the example I'm talking about

http://sbhepnt.physics.sunysb.edu/~rijssenbeek/PHY134_Induction.html

The first part is correct. A changing AC B field is just the same as the DC case with a time dependence.

But I'm a little dubious about your use of 'intensity' in this context. The B field is a statement about force. meaning that 'if a monopole were placed at this position, it would experience a force of this magnitude'
Intensity is something else, it's the square of an amplitude. Fair enough, if you wanted to talk about the intensity of the oscillation in the (static) B field, you might use this concept, but the field you are talking about is so weak that it's of little or no practical interest.
I've never thought about it, but I guess this perturbation in the local field of a coil should exist (as a slight superimposition on the EM fields) whether you would be able to actually detect or measure it is questionable.

 

[azaharak]

thanks again

Your right about the intensity, I am stupid for saying that.

Can't really associate static B field with intensity.
-------------------


Back to what your saying about the helmholtz sinusiodal B field acting as a perturbation in the EM field... Are you saying that if you were to measure B and E components along the axis of the coil, that the EM radiative field would be more dominant?

In this lab experiment

http://sbhepnt.physics.sunysb.edu/~r...Induction.html

the field is measured using a second coil coupled to an op amp amplifier circuit. The current induced is proportional to the B field at that point along the axis. If the current is plotted vs the inverse of the spatial depence, we can infer a linear relationship. I've done this experiment before.. it works. But where the heck is the r squared field then, i didn't measure that kinda dependence. I know I am measuring B (comparitively) and Not intensity, but then shouldn't the B field fall off 1/r if light is supposed to have a inverse square dependence?


secondly...

I feel that we would be "double counting" the magnetic field if we added it to what the EM radiative field does at any point along the axis.

Let the Ac current be ON for one cycle, this creates a changing B field creating an E field which in turn creates a B field and vice verse propagating down the axis. If we stop curren,t we stop the B field, whatever is left will proprogate down the axis, the EM radiation stops.


Help me to understand this... thanks again

 

[AJ Bentley]

Are you saying that if you were to measure B and E components along the axis of the coil, that the EM radiative field would be more dominant?

You're asking questions I'm not really qualified to answer. I know the usual derivations of the fields etc, but this is an unusual configuration.
Normally EM is theoretically produced by an oscillating charge, ie an oscillating E field rather than a B field. However, I see no reason why it shouldn't be done this way except that it will be very inefficient.
It's easy to provide a large, rapidly changing voltage to an aerial (effectively a low capacitance capacitor), but for a magnetic coil, you need to provide a large, rapidly fluctuating current to a high inductance coil - not easy.
However, the difference between a 1/r^2 component and a 1/r^3 component is huge. So I have to answer yes. At very low frequencies where the EM emission has little energy in it, you should be able to detect the dipole field close to the coil.

where the heck is the r squared field then,

The EM radiation produced is dependent on the rate-of-change of B field, which will be inversely proportional to inductance. Since your experiment is designed to produce a relatively large B field in order to measure it (i.e high inductance), EM radiation will be weak (I said before that it would be inefficient).
Then again, the energy in the radiation depends on frequency. At frequencies where you might be able to see a compass needle swing, there is virtually no power available to affect the needle. (Same is true of a Hall effect sensor). EM gets more energetic as you increase frequency.
You have an equipment problem. in the region we're talking about, conventional EM detectors have problems too. I've never heard of anyone trying to detect EM frequencies below a few kilohertz - even though in theory the radiation must exist. You would have to invent a new type of detector.

I feel that we would be "double counting" the magnetic field if we added it to what the EM radiative field does at any point along the axis.

Well, we're not 'adding' the two. The static B field is what it is in the static case. The EM
radiation is a fluctuation of that field.
It's the difference between the movement of a body of water and the waves that travel on it.
In order to produce the EM radiation you have to vary the coil input current down through zero, reverse it's direction, up in the other direction, then swing it back again. That produces a ripple just as if you were to somehow grab the B field and shake it up and down.
Your static experiment measures the 'height of the water surface' but can't see the ripples. (mainly because you're not making any - but even if you tried to do so, the experiment configuration is hopelessly wrong to make and/or detect them as I said before)

 

[azaharak]

I really appreciate your efforts... You have been very helpful


doesn't the time varying current in the wire still constitute an oscillating charge or electric field? Current is a wire means that there is an electric field (related by the conductivity).

Ok so Now I think I get it... Please correct me If I am wrong

The "Diplole" radiation (time varying current making the time carying magnetic field) falls off with 1/r^3. Sufficiently close to the coil (r<1) this will dominate the detectable B field along the axis.

Now for the the radiation from the oscillating charges (alternative electric field in the wire). If we individualized each one of those charges they would be creating some kind of field ( the intensity would fall off with (1/r^2) so this means that the B or E fields they create will fall off with (1/r) because the Intensity is related to the amplitude squared.


This field is sufficiently small for r<1 compared the other dipole field.
.....

Now you said that the radaition from the oscillating charges increases with the frequency, so I am assuming that it will dominate at greater frequencies.

In fact I just found an area in griffiths that treats this. (I think) Chap 11 pg 452-454 if you have the 3rd edition. He discusses magnetic dipole and electric dipole radiation. Although I am not sure we would have electric dipole radiation here, it says that in the limit R<<c/w (the radius is much smaller than speed of light divided by angular frequency), then the electric dipole radiation should dominate (unless when the system is carefully contrived such as this case) then the magnetic dipole radiation will reveal itself.

But I don't think our scenario would constitute electric dipole radiation, merely the radiation from moving point charges.

In any event, I think I understand that this is merely a situation of dominating effects at a particular distance due to low frequenculy & proximity along coil axis.

Thanks again



I also remember they use a double Helmholtz coil in NMR to create RF that flips the spins in the sample your analyizing.

 

[AJ Bentley]

You've got it near enough for the moment. Your understanding of this stuff will refine with time.
There's tons more to learn about these fields, some of it is absolutely amazing. Don't get bogged down in detail. Try to skim the surface. Eventually it all comes down to a single concept - which can be expressed as a single equation. But you need to understand a whole bunch of other stuff about quantum mechanics and relativity before it makes sense.
Until then you just have parts of the jigsaw puzzle - don't try to hammer the bits together, it won't work!

Any movement of charges can be taken to be dipole radiation, the term dipole is just a reference to the easiest formal analysis of EM radiation.
As we've been discussing, radiation can arise from the analogous magnetic case of a simple inductor.

 

[azaharak]

Thanks


Sadly I've taken QM and REL, both undergrad and grad and others. I can do the math, and that's all that was ever taught really. There always seems to be a large disconnect between what's on the paper and trying to explain something, that's what I've been trying to conquer lately.

 

[AJ Bentley]

Take a look at the YouTube videos from Stanford U.

http://www.youtube.com/watch?v=BAurgxtOdxY&feature=channel"