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What are the magnetic field lines basically depicting in terms of moving charges or charge carrier particles or currents.

What do those circular loops around a straight current carrying wire actually tell us? Do they provide information regarding direction and flow of currents?

Do magnetic lines of force depict path of moving charges or their velocity field or axes of rotation?

NB: I already know that magnetic lines represent the directions in which a compass needle or magnetic monopole (if one existed) and also that it signifies the direction of vector B. This in textbooks all over the place.(this is not the information I am seeking).

Now to go one step further may I ask what does this "direction of the magnetic field ⃗B" physically signify/indicate.

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    $\begingroup$ You have two answers that you have rejected with the same complaint: Thanks for the answer but I knew this already. Its in textbooks all over the place. Now may I ask what does this "direction of the magnetic field ⃗B" physically signify/indicate. It's not clear to me what you're really looking for here. It seems like you want someone to deny the correct information that you've read in textbooks and confirm your incorrect idea that the field is somehow a material phenomenon like the flow of charges. $\endgroup$ – user4552 Nov 4 '18 at 18:46
  • $\begingroup$ @user579908: The magnetic field is a vector at every point in space. A vector has magnitude and direction, and remains invariant under coordinate transformations. When you take the cross product of the velocity vector and the magnetic field vector, it gives the force experienced by a charged object. That's its physical significance. It is difficult to tell what kind of answer you are looking for. $\endgroup$ – user7777777 Nov 5 '18 at 5:45
  • $\begingroup$ I've flagged this question as "unclear what you're asking". $\endgroup$ – user7777777 Nov 5 '18 at 5:51
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The magnetic field lines give the direction and intensity of the magnetic field $\vec B$. The magnetic force is given by the Lorentz force, $\vec F = q \vec v \times \vec B$. So the field lines do not directly give the direction of the force nor the direction of motion, but these can be derived from them.

By the way, magnetic monopoles do not exist and also a monopole can not point in any direction.

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  • $\begingroup$ Thanks for the answer but I knew this already. Its in textbooks all over the place. Now may I ask what does this "direction of the magnetic field ⃗B" physically signify/indicate. $\endgroup$ – user579908 Nov 4 '18 at 18:38
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Magnetic field lines simply indicate the direction of the magnetic field $\vec{B}$. (And the spacing of the field lines indicates the magnitude of this field.) They do not indicate the direction of current, or the path of moving charges, or any kind of velocity field or axis of rotation.

Using the Lorentz force law $\vec{F}=q(\vec{E}+\frac{\vec{v}}{c}\times\vec{B})$, you can figure out how the magnetic field lines exert force on a moving charge. Because of the cross product, the force is perpendicular to the magnetic field lines, and also perpendicular to the velocity.

For example, consider a positive charge moving parallel to a wire carrying a current. (I mean moving in space outside the wire.) The field lines loop around the wire, but they exert a force on the charge that is directed radially away from the wire.

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  • $\begingroup$ Thanks for the answer but I knew this already. Its in textbooks all over the place. Now may I ask what does this "direction of the magnetic field ⃗B" physically signify/indicate. $\endgroup$ – user579908 Nov 4 '18 at 18:36
  • $\begingroup$ The "direction of the magnetic field" physically indicates nothing more and nothing less than the direction of the magnetic field. Fields are as real as matter, but are not made of matter. Don't expect a field to be anything other than a field. You can calculate other things, like forces and energy densities, from the field, but you should not think that these are more "real" than the field is. $\endgroup$ – G. Smith Nov 4 '18 at 21:37
  • $\begingroup$ If a magnetic field physically signified something other than a magnetic field, this would have been mentioned in your textbooks. In current physics, fields are ontologically fundamental objects that are themselves and nothing more. $\endgroup$ – G. Smith Nov 4 '18 at 21:44
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What do those circular loops around a straight current carrying wire actually tell us? Do they provide information regarding direction and flow of currents? Do magnetic lines of force depict path of moving charges or their velocity field or axes of rotation?

No, none of the above. Magnetic fields can exist in a vacuum. They aren't material.

The magnetic field loops in your example are a way of representing a vector field, which looks like this:

magnetic field vectors

This picture is in a plane perpendicular to the wire, with the current coming out of the page. Each of these vectors represents the strength and direction of the magnetic field at that particular point. The representation in terms of field lines is simply a visual way of linking up the arrows; it's an intuitively appealing representation that is also quicker and easier to draw than the "sea of arrows" representation.

I already know that magnetic lines represent the directions in which a compass needle or magnetic monopole (if one existed) would point, (this is not the information I am seeking).

OK, but this is basically the style of definition that we use when defining field vectors.

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  • $\begingroup$ Thanks for the answer but I knew this already. Its in textbooks all over the place. Now may I ask what does this "direction of the magnetic field ⃗B" physically signify/indicate. $\endgroup$ – user579908 Nov 4 '18 at 18:38
  • $\begingroup$ There is a fundamental force called the EM (electromagnetic force) that scientists study and it is observed as an electric charge force and magnetic force. After studying the magnetic force they know if they assign it a direction based on how it effects electrons and other magnets, then they can use this consistent direction definition to make all kinds of correct calculations of the force. If an electron takes a curved path (with no E-field present) the magnetic force direction can be ascertained, also a compass is another easy way. $\endgroup$ – PhysicsDave Nov 4 '18 at 21:33

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