Understanding Electro Magnetic Field

It is called an electromagnetic field because the field energy will reside as both a magnetic and electric field unless you have a static condition. Also you are improperly mixing units that shows that you need to go back to your text books for a better understanding of the fundamentals. The electromagnetic force (emf) is measured in the unit of Volt. Electrons have a fixed unit of charge measured in coulombs. Fifty electrons will have about 8*10^-18 coulombs of charge in total. Current is the number of coulombs of charge per second. Now if you do the algebra, one ampere of current for one second means that about 6.24*10^18 electrons will have passed by that point in one second. Trying to track 50 or 100 discrete electrons will get into the realm of quantum mechanics. A realm you are not ready to discuss.

To make it simple: there is no ready path from quasistatic electric and magnetic field to the understanding of the electromagnetic phenomenon.The physicians in the previous century had a hell of a difficult time with it. Without Maxwell's mathematical genius we might have another century's worth of trouble with it.

If you are really determined, take an relatively uncomplicated work starting with the Maxwell equations. Work, wrestle, and absorb them. Then, at least you have a cookbook level of knowledge. And go from there. The best is to treat it as a foreign language with a different alphabet, different world view.

You will have to learn, what IS. For example, in EM asking the question, if E causes M or the other way around only leads you into logically untenable situations.

Forget it, go for broke.

Are you the same Anonymous Poster of this thread? Even if you aren't maybe you can get together....

http://cr4.globalspec.com/thread/72015#newcomments

From your question I guess that you have a problem in understanding the transient phenomena. Instead of solving equations, build a simple circuit, apply a burst sinewave from a function generator using, say, 10 full waves and an equally long pause between the packets, and use a multichannel oscilloscope to view the voltages and currents (you can use resistors of 100× smaller value in series with the circuit components to monitor the currents). If you set the frequency of the generator to the characteristic frequency of the circuit, or slightly above, you will be able to see what is going on: as the generator starts from zero, the currents in the circuit having a complex impedance will undergo a phase modulation within the first half period of the waveform, after which the phase shift remains constant and the appropriate "steady state" relations are established. You may also use a PC circuit simulation program if you have one, and do it in the virtual world, where it might be more flexible to adjust the circuit parameters.

After you understand what is going on you may want to solve some equations, but you will need to work in time domain to obtain the transient response, from the frequency domain you only get the steady state solutions. It is of course possible to use the inverse Fourier or Laplace transform, which is easier than solving differential equations, but you still need to understand the method.

If you want to master this, I can recommend a book titled Wideband Amplifiers, by Starič and Margan (Springer Verlag), available also from Amazon, in which you can find everything, the analytic and the numerical methods well explained. Enjoy.

Emf stands for electromotive force, not electromagnetic force.

I am the same author of the other post there was given a link to.

Slowlight, do you meant the transition is happening rather gradually , for the first several periods after switching on the source, not after the first one ?

All changes occur gradually, depending on the system upper cut-off frequency. An abrupt change would imply an infinite bandwidth and infinite energy impulse.

In simple single-pole RC or RL circuits the phase change occurs within the first half period of the input waveform, (assuming the sinewave is being switched on at the zero crossing). But the whole thing is both freqency-dependent and system dependent (i.e., if the system has many compplex-conjugate poles and no real dominant pole you can get long ringing in both amplitude and phase response).

I gave you the example of the single pole system because that was your first question, and also because such a system is more easy to analyse and comprehend. More complex cases will be more ...er... complex;o)))

Assuming phase change (90 degrees) between

1. sine wave of the emf starting at zero and

2. electrons starting moving

occurring at the first half period of the wave of emf,

but, at which point flux starts?

Again, the phase change is gradual, not an immediate 90° lag or lead. Imagine a step function applied to an RL circuit. The current through L will change in time in an exponential manner (either e^(-tR/L) or 1-e^(-tR/L), depending on the circuit configuration). By switching on a sinewave at its zero crossing, your input function is effectively a multiplication of the unit step and the sinewave, and the same must hold for the response. So your response to a switched sinewave will be a multiplication of an exponential and a sine function, which, using trigonometric transformations, can be separated into an amplitude function of time and a phase function of time.

So the "flux" starts immediately, but slowly, then it soon changes direction as the applied sine voltage reaches its peak and finally settles to the appropriate value.

The suggestion made by Rixter about inertia may help you to build a mental model.

But as I said before, don't wrestle with mental models; try it and it will all be immediately clear.

Dear Slowlight, are you typing the phrases from the book you referred to earlier, or are they your own thoughts ? What is "unit step" ?

Could you please elaborate a bit about how

the "flux" starts immediately, but slowly, then it soon changes direction as the applied sine voltage reaches its peak and finally settles to the appropriate value.

Dear Anonymous Poster #1,

After two threads and umpteen posts which Steinmetz would have found difficult to answer, we, the CR4 experts, will not answer till you become "Onymous".

As you can see, two can play at this game.

Anonymous AH

Sorry for the late answer and sorry for using jargon (after ~45 years in this business, it is hard to avoid, especially when by the relevance of the question one assumes that the person asking it has more experience).

The unit step is the current or voltage jumping from one level to another within a time much shorter than the shortest time constant of the system under investigation, and it does so now and never again. For mathematical simplicity it is ordinarily assumed that the previous level is zero and the final level is one, hence the name (coined by Oliver Heaviside back in ~188x). Of course, in practice it is approximated well enough by a low frequency square wave. More on Wikipedia.

And I have already "elaborated" enough on the flux time function, saying that it is a multiplication of an exponential and sinusoidal function. Now it's up to you to make the circuit, in either the material or virtual world, and test it to check if that is satisfactory description or not.

If electrons are moving there is current and as soon as current exists there is magnetic flux around any conductor that is carrying current..

Current (and thus flux) may be delayed by a long time-constant L/R.

RHABE

Here is a mechanical analogy to help you understand what is going on. Motion = current, Force = voltage. Put your hand in a bucket of water and move it around. The faster you move your hand, the more force is required. This is analogous to applying a voltage across a resistor.

Now hold a 10 pound weight in your hand. It requires force to start it moving and also requires an opposite force to stop it. Applying a voltage across an inductor starts the current moving and an opposite voltage is required to make it stop. This is why the current and voltage are 90 degrees out of phase for an inductor.

An inductor resists change in current the same way a weight resists change in motion. The reason is that as current increases, the magnetic flux increases. This flux acts on the coils in the inductor to create an apposing voltage called back emf. So you have to apply a voltage to increase or decrease the current through an inductor.

There could be

the quicker you move the 10 pound weight in your hand the more force is required. This is as voltage across a resistor, and

when you stop your hand moving in a bucket of water an opposite force is required to stop moving water around you hand. This is inductor and 90 degres voltage / current shift.

Sorry Rixter if I sounded impolite in my post 14, no offence to you was intended, only I found the examples little explanatory.

When an electron moves in a conductor, a magnetic flux is created. When the electron stops moving, the magnetic field collapses to zero. Any movement, no matter how small, will produce a magnetic field, also appropriately small. I hope this answers your question.

It might seem a bit oblique, but I think this is interesting and germane to this thread (albeit a bit long).