Charge moving with a constant linear velocity....

[Maciej Orman]

If you can create a greater rate of charge flow ( current) then you will get a bigger magnetic field. But aren't you suggesting that an accelerated charge is needed as in, for example, Rowlands experiment?

Not suggesting, magnetic field due to accelerated excess charge is basic knowledge... What is missing is magnetic field due to constant linear velocity motion in straight line of excess charge experimental evidence... Logic suggests that since constant linear motion can only be visible in relative to other bodies then magnetic field created due to such motion and proportional to the velocity cannot exist since it would define an absolute motion and absolute speed measuring method...

 

[vanhees71]

You don't need acceleration. A steady current also gives a magnetic field. Usually you start with that simpler special case when learning electrodynamics, namely with electrostatic and magnetostatic fields. What you get in addition when charges are accelerated (i.e., charge-current distributions become time-dependent) is electromagnetic radiation in addition to the static field around any charge.

 

[Maciej Orman]

You don't need acceleration. A steady current also gives a magnetic field. Usually you start with that simpler special case when learning electrodynamics, namely with electrostatic and magnetostatic fields. What you get in addition when charges are accelerated (i.e., charge-current distributions become time-dependent) is electromagnetic radiation in addition to the static field around any charge.

Steady current? You mean DC current in wire? If so, then such represent accelerated motion of electrons and such motion is never in straight line...

 

[A.T.]

...maximum charge on the belt reaches a magnitude of several orders larger than in normal operation of the VDG...

Any actual numbers on the charge and velocity of the VDG versus charge and tangential velocity of the Rowland disc?

Logic suggests that since constant linear motion can only be visible in relative to other bodies then magnetic field created due to such motion and proportional to the velocity cannot exist..

No, it just suggests that this magnetic field would be frame dependent.

 

[Ibix]

Not suggesting, magnetic field due to accelerated excess charge is basic knowledge...

Reference, please. Note that simply citing the Rowland disc is not sufficient, since the results are entirely explicable in terms of the linear speed of the charges (see p98-9 of https://books.google.co.uk/books?id...B#v=onepage&q=rowland disc experiment&f=false).

Note that the numbers quoted there suggest that Rowland was able to detect an incredibly small magnetic field, but there is no suggestion that the acceleration was relevant.

Logic suggests that since constant linear motion can only be visible in relative to other bodies then magnetic field created due to such motion and proportional to the velocity cannot exist since it would define an absolute motion and absolute speed measuring method...

...or, the magnetic field could be frame-dependent.

 

[Maciej Orman]

Any actual numbers on the charge and velocity of the VDG versus charge and tangential velocity of the Rowland disc?

No, it just suggests that this magnetic field would be frame dependent.

Only at relativistic speeds...

 

[vanhees71]

Steady current? You mean DC current in wire? If so, then such represent accelerated motion of electrons and such motion is never in straight line...

I've given the formula for a particle in unaccelerated uniform motion. In the reference frame, where the velocity doesn't vanish, the electromagnetic field has both electric and magnetic components. You don't need accelaration of charges to get a magnetic field. That's all I'm saying, and it follows straight-forwardly from Maxwell theory!

 

[Ibix]

Any actual numbers on the charge and velocity of the VDG versus charge and tangential velocity of the Rowland disc?

According to the link in my previous post, Rowland had a 20cm diameter ring charged to 10^-7C spinning at 50 revs/s. And was able to detect a magnetic field from it, which suggests epic experimental skills to me.

 

[vanhees71]

...or, the magnetic field could be frame-dependent.

The electromagnetic field is described by a 2nd-rank tensor and thus frame-independent. The split into electric and magnetic components of course is frame-dependent.

 

[Maciej Orman]

I've given the formula for a particle in unaccelerated uniform motion. In the reference frame, where the velocity doesn't vanish, the electromagnetic field has both electric and magnetic components. You don't need accelaration of charges to get a magnetic field. That's all I'm saying, and it follows straight-forwardly from Maxwell theory!

Yes, except this is only a theory and if such was true we would have a method of absolute speed measuring using excess charge body as a sensor...

 

[Ibix]

Yes, except this is only a theory and if such was true we would have a method of absolute speed measuring using excess charge body as a sensor...

No you would not. For the reason I've given twice, and vanhees71 and A.T. have given at least once each.

 

[Maciej Orman]

According to the link in my previous post, Rowland had a 20cm diameter ring charged to 10^-7C spinning at 50 revs/s. And was able to detect a magnetic field from it, which suggests epic experimental skills to me.

No, triboelectric charging method creates volume charge for which there is no method of measurement... Thus suggesting that the charge is much larger than estimated...

 

[Ibix]

No, triboelectric charging method creates volume charge for which there is no method of measurement... Thus suggesting that the charge is much larger than estimated...

Reference please.

 

[vanhees71]

Reference, please. Note that simply citing the Rowland disc is not sufficient, since the results are entirely explicable in terms of the linear speed of the charges (see p98-9 of https://books.google.co.uk/books?id=MbSUqqzFDocC&pg=PA98&lpg=PA98&dq=rowland+disc+experiment&source=bl&ots=0OzuvkesWW&sig=G_oqn3m8UNNQmnz97pz9_tQXVyQ&hl=en&sa=X&ved=0ahUKEwiI3dfXo_LVAhWGC8AKHbvyCWsQ6AEIDTAB#v=onepage&q=rowland disc experiment&f=false).

The point of Rowland's experiment (and other similar experiments in the late 19th century) was to proof that electric currents are due to moving charges ("electrons"). Nowadays that sounds trivial, because according to our present understanding all electric currents (and magnetizations) are due to elementary particles, but at this time the very nature of electric charges and currents was not that clear.

If I understand the excerpt from the textbook right, you have a charged ring of radius $R$. The corresponding current density is
$$\vec{j}(\vec{x})=\rho \vec{v}=\frac{q}{2 \pi R} \delta(\varrho-R) \delta(z) \omega \varrho \vec{e}_{\varphi},$$
where $(\varrho,\varphi,z)$ are standard cylinder coordinates. The corresponding magnetic field can be calculated using the vector potential (in Coulomb gauge),
$$\vec{A}(\vec{x})=\frac{1}{c} \int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x} \frac{\vec{j}(\vec{x}')}{4 \pi |\vec{x}-\vec{x}'|},$$
and finally the magnetic field as
$$\vec{B}=\vec{\nabla} \times \vec{A}.$$
The integral can be found in some good textbooks (like Jackson), leading to elliptic functions.