Electromagnetic Field Theory

[paleolithic]

Does anybody know of any good reading material on the electromagnetic field theory? Internet, books, articles, anything?

[swansont]

I thought David J.Griffiths' Introduction to Electrodynamics text was pretty good. At a higher level, Jackson's Classical Electrodynamics is the standard graduate text.

[calbiterol]

Would you happen to know any websites, for a start?

[swansont]

Hyperphysics Concepts is a good resource for all sorts of basic physics.

[quick silver]

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nucnot.html#c2

 

try this site. you will have to go back to the home page to find the Hyper-physics page. it has everything there. astrophysics-quantumphysics.

 

this should be of some help to you.

 

good luck

[S. Herzman]

The naval engineering text has a decent section on electromagnets. It is amazing what you can do with a magnet.

[paleolithic]

Thanks a lot everybody, I'll get on those immediately.

[labview1958]

Can a permanent magnet be modelled as a current carrying wire? If have a cylindrical magnet of strength 0.1 Tesla, length 3 cm and radius 1 cm., can I take a wire of length 3 cm, radius of 1cm and pass y Amps of current. Can I model it that way? Or is there a better model!

[swansont]

Can a permanent magnet be modelled as a current carrying wire? If have a cylindrical magnet of strength 0.1 Tesla, length 3 cm and radius 1 cm., can I take a wire of length 3 cm, radius of 1cm and pass y Amps of current. Can I model it that way? Or is there a better model!

 

You can't model it as a straight wire because the field doesn't go in the correct direction. You can try and model it as a loop of wire, or as a series of loops (solenoid).

[Johnny5]

Can a permanent magnet be modelled as a current carrying wire? If have a cylindrical magnet of strength 0.1 Tesla, length 3 cm and radius 1 cm., can I take a wire of length 3 cm, radius of 1cm and pass y Amps of current. Can I model it that way? Or is there a better model!

 

I think permanent magnetism has something to do with some kind of regularity in the way all the dipoles are aligned.

 

In non-magnetic matter, the orientation must be somewhat random, and so magnetic effects just tend to cancel out, which would explain why a powerful refridgerator magnet does not attract a piece of paper.

 

A normal wire is non-magnetic.

 

Once you "pass current" through it, it will demonstrate very weak, mild magnetic effects. For example, Oersted noticed that if he placed a compass near a wire, and then "passed current" through the wire, the compass needle moved.

 

So a changing electric field leads to a magnetic field. I don't know how else to say that.

 

And there are some very simple formulas, from classical electrodynamics, which would tell you the B field created by a current carrying wire, in the region of space external to the wire.

 

Directly from the Biot-Savart law we have:

 

[math] \vec B \equiv \frac{\mu_0}{4 \pi} \int \vec J \times \frac{\hat r}{r^2} d \tau [/math]

 

mu_0 is the pearmeability of free space.

 

J is the volume current density. There is also line current density, which is represented by lambda, and surface current density, which is represented by lower case sigma. Which you use, depends upon your particular configuration.

 

In modelling your current carrying wire, you have to decide whether or not you are going to use J or lambda.

 

A real wire is three dimensional, so J would be more appropriate, if you are going to investigate field effects near the wire. On the other hand, if you are mainly concerned with field effects far from the wire, lamba is fine, and I think the mathematics is simpler that way.

 

But I am not sure what you are trying to do.

 

Now, the most elementary problem in Magnetostatics, would be an infinitely long wire carrying a constant current i. And then to a good approximation, you will use V=voltage = iR. Again I am not sure exactly what you are out to do.

 

You can use ampere's law to figure out the B field quite easily, and you can also go through the mathematics using the Biot-savart law to get the field of the current carrying wire. Both approaches yield the same answer, so find the B field using both methods.

 

The end result, from memory, is that the B field wraps around the wire in a circular fasion, and decreases as you move away from the wire.

 

B is inversely proportional to the distance you are away from the wire, so the field effects fall off as 1/r.

 

Now, in the case of a permanent magnet, the field does not wrap around in circles.

 

The shape is famous, it's toroidal. There is a north pole, and a south pole.

 

The magnetic field lines go from one pole to the other, and have a sort of elliptical shape to them.

 

Now, if you have some good intuition about magnetic fields, you can "build up", so to speak.

 

Once you understand the formula for the magnetic field of an infinitely long wire, then you can progress to the solenoid, as Dr. Swanson suggested.

 

I recommend you do this too.

 

Solve the following problem next, wrap a wire around a cylinder, N times, in circles, going up to the top of the cylinder, and back down, and back up.

 

You will know the current in the wire, you will know the magnetic field contribution from tiny portions of the wire, and because the wire has been wrapped around a cylinder, there will be a NET magnetic field, all due to the wire geometry.

 

From memory, the approximate answer is:

 

[math] B = \mu N i [/math]

 

Along the axis.

 

Find a clear presentation.

 

But my point is, your intuition can tell you what the field will be, if you already understand the answer to the infinite current carrying wire.

 

And then, you can wrap a solenoid into a huge circle, to get a toroid.

 

And again, your intuition and the mathematics should agree.

 

I would suggest developing your model in stages.

 

Each stage being more accurate than the previous one.

 

Regards

[Meir Achuz]

The PM can be modeled as a solenoid with a current carrying wire wrapped around it. In fact, this is just what happens to the molecular currents that cause the magnetization. They cancel in the interior of a bar magnet, but circle the outer surface.

[labview1958]

According to Bio-Sarvat Law regarding a long curent carrying wire, the field is given by

B = MU(o)I/2*3.142*r where r is the distance from the wire. It says that the FIELD is inversley proportional to the distance. However we know that the FIELD of a permanent magnet varies as an inverse CUBE. If I model the permanent magnet as a solenoid what would be the SIMPLE formula?

[Johnny5]

According to Bio-Sarvat Law regarding a long curent carrying wire' date=' the field is given by

B = MU(o)I/2*3.142*r where r is the distance from the wire. It says that the FIELD is inversley proportional to the distance. However we know that the FIELD of a permanent magnet varies as an inverse CUBE. If I model the permanent magnet as a solenoid what would be the SIMPLE formula?[/quote']

 

Here is the first site that I found with the answer:

 

Magnetic field of a solenoid

 

About a year ago, I found a site with a far more complicated approach, and a different answer than the simple:

 

B = m N i

 

i will look for it.

 

At any rate, the formula above comes out of the Biot-Savart law, or Ampere's law (which is the simplest way to get it).

 

I haven't read through the link above, but that site is an excellent source for almost any topic of physics.

 

If you want me to derive the formula using either Ampere's law or the Biot-Savart law, let me know.

 

It doesn't take too long.

 

Regards

 

 

 

Here is a link which shows that the fields are similiar:

 

B fields permanent magnet/solenoid

[swansont]

Here is the first site that I found with the answer:

 

Magnetic field of a solenoid

 

About a year ago' date=' I found a site with a far more complicated approach, and a different answer than the simple:

 

B = m N i

 

i will look for it.

 

At any rate, the formula above comes out of the Biot-Savart law, or Ampere's law (which is the simplest way to get it).

 

I haven't read through the link above, but that site is an excellent source for almost any topic of physics.

 

If you want me to derive the formula using either Ampere's law or the Biot-Savart law, let me know.

 

It doesn't take too long.

 

Regards

 

 

 

Here is a link which shows that the fields are similiar:

 

B fields permanent magnet/solenoid

 

I think he wants equations for the off-axis solution, that show the dipole nature.

[Johnny5]

I think he wants equations for the off-axis solution, that show the dipole nature.

 

I can't find the derivation. Can you send me a link in which the off axis solution is derived?

[swansont]

I can't find the derivation. Can you send me a link in which the off axis solution is derived?

 

I couldn't find one online in a limited search. I know I have done it for Helmholtz coils and plotted the field, but that was a few computers ago, so those files (and the application) may be long gone.

[Meir Achuz]

The magnetic field on the z axis of a solenoid (in Gaussian units) is:

B=[2\pi(N/L)I/c][sin A_2-sin A_1], where A_i is the angle between a line perpendicular to the axis of the solenoid at one end and a point on the z axis. If you write this in terms of z and expand, you can use Legendre polyomials to find the field off the axis and the dipole moment of the solenoid.

[Meir Achuz]

I should have mentioned that the magnetic moment of a solenoid is much easier: \mu=NIA/c, where A is the cross-sectional area of the space inside the coils.

If you don't like Gaussian units let 1/c-->mu0/4pi.

[Johnny5]

I couldn't find one online in a limited search. I know I have done it for Helmholtz coils and plotted the field, but that was a few computers ago, so those files (and the application) may be long gone.

 

Yeah neither could I.

[Johnny5]

The magnetic field on the z axis of a solenoid (in Gaussian units) is:

B=[2\pi(N/L)I/c][sin A_2-sin A_1]' date=' where A_i is the angle between a line perpendicular to the axis of the solenoid at one end and a point on the z axis. If you write this in terms of z and expand, you can use Legendre polyomials to find the field off the axis and the dipole moment of the solenoid.[/quote']

That sounds familiar. I think Griffiths did exactly that, I don't have my book with me but I will check later.

 

Regards

[Tom Mattson]

Boy oh boy, you guys couldn't find a needle in a stack of needles!

 

Fortunately one of my hobbies is scouring the web for downloadable freebies.

 

Voila: http://www.plasma.uu.se/CED/Book/

 

This happens to be the first hit if you type "electromagnetic field theory textbook" into Google, which apparently no one did!

[labview1958]

Whatever the suggested formula, it must be remembered that a permanent coil does not have N ( number of coils). Thus those equations cannot be used. Is there any other way?

[labview1958]

Anyway the formula :

B = mu*N*i

only gives the FIELD in the centre of the magnet. What about the field at "z" distance from the solenoid. Furthermore the magnet does not have "N" turns of the coil.

[swansont]

Whatever the suggested formula, it must be remembered that a permanent coil does not have N ( number of coils). Thus those equations cannot be used. Is there any other way?

 

 

But if you're tring to model the magnet, it has to be by a coil. NI is the total current. You can use more current and fewer turns, or less current and more turns, but you get the same answer.

[labview1958]

Is this correct?

B = mu*N*I = mu*total current

 

This means there is no difference between a solenoid model and a current filament model!