# Magnetic field

## Main Question or Discussion Point

If a cylindrical magnet with a uniform magnet field were to be rotated at high speed along its polar axis (assuming the poles to be at either end of the cylinder) would there be any change or distortion to the shape (ie pattern of field lines) of the magnetic field?

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If the cylinder is perfectly uniform that rotating it along its axis will not make a difference at all due to symmetry. If I give you a perfectly uniform cylinder, you could not see whether it was rotating or not.

If the cylinder is perfectly uniform that rotating it along its axis will not make a difference at all due to symmetry. If I give you a perfectly uniform cylinder, you could not see whether it was rotating or not.
The question is whether the rotation of the cylindrical magnet will change the shape of the magnetic field surrounding the magnet.

Since I stated that the magnet is to be rotated there is no doubt about the rotation.

Then I ask another question: if there is no physical difference between your cylinder rotated 0 degrees, and your cylinder rotated 59.3958193 degrees, what would cause the magnetic field surrounding it to change?

I was not trying to tell you that you cannot rotate it. Of course you can, but you cannot see it rotating (it is not physically different if it is rotated).

I don't think Nick's answer is correct, since if you have a charged sphere, the EM field changes even though it is perfectly rotationally symmetric. In fact, the system produces magnetic field and will radiate if the rotational speed changes in time.

My answer to the original question is: No or Maybe...

Using maxwell's eq, Given B and E, we can find the current density. In this case, there is a surface current moving around the cylinder to produce the magnetic field. E=0 so that the net charge is zero. If you rotate this cylinder at a uniform speed, the current caused by the positive charge increases, However, this is canceled by the new current caused by negative charges, so that J stays the same and hence B is unchanged.

Now, if you are speaking of relativistic speed... then I don't know. It depends on how the rotation is applied and how J is changed. Actually, even in the previous case, it depends on what you mean by rotation, do you mean every single particle in the cylinder moves with an additional speed? or something else?

Oh, I completely missed the point that it stayed in rotation...! I thought you just rotated it and asked if the magnetic field was the same after rotation then it was before rotation.

If you are actually rotating it all the time then the magnetic field may change because the current that causes it will speed up. I'm not too sure about this to be honest... I don't think it will change if it is rotating at constant speed, but if it is accelerating there will most probably be a change (it basically becomes an EM-radiator).

Thanks for the replies. I am not aware of Maxwells equations being able to describe the "shape" of a magnetic field.

What Iwould like to know is supposing the field lines are traced when the magnet is stationary and if they were traced again when the magnet is rotating at a very high speed would there be any difference in the patterns of the field lines?

well, Maxwell's eq is THE equation that describe all of electric and magnetic field. It tells you the shape, the strength and the direction of all kinds of electromagnetic fields.

The straight answer to your question is no, and the explanations were given in my first post.