Magnetic field and moving charge special relativity

[Herbert11]

Hi. In a current carrying conductor because of special relativity amount of protons and electrons differ so we get an electric field or as we call it magnetic field. So if magnetic field is just an electric field how is it that the charge has to move so that magnetic field would exert a force on it? Electric field doesn't require that.

 

[PeterDonis]

In a current carrying conductor because of special relativity amount of protons and electrons differ

Why do you think so?

so we get an electric field or as we call it magnetic field

They're not the same thing, and I have never seen a reputable source (textbook or peer-reviewed paper) call them the same thing.

if magnetic field is just an electric field

It isn't.

Where are you getting your understanding from?

 

[Dale]

if magnetic field is just an electric field

A magnetic field is not just an electric field. Both the electric field and the magnetic field are components of the electromagnetic tensor. Neither one can claim supremacy or priority over the other.

 

[Nugatory]

In a current carrying conductor because of special relativity amount of protons and electrons differ so we get an electric field or as we call it magnetic field.

This is Edward Purcell's explanation of how magnetic fields arise from length contraction; you'll find a reasonably complete explanation of it here: http://physics.weber.edu/schroeder/mrr/mrrtalk.html. This is by no means a complete explanation of how magnetic fields arise; it is best thought of as a physical motivation for the more abstract and powerful methods that @Dale mentions above.

how is it that the charge has to move so that magnetic field would exert a force on it?

The number of positive and negative charges in a given length of the current-carrying wire is, because of special relativity, frame-dependent. Only if the charged test particle is moving relative to the wire will the relativistic effects lead to an imbalance between the number of postive and negative charges, and hence a force on the test particle.

 

[Ibix]

So if magnetic field is just an electric field

As noted by others, it isn't. If an electromagnetic field can be described as pure electric field in one frame then there is no frame in which it is a pure magnetic field, and vice versa.

 

[pervect]

Hi. In a current carrying conductor because of special relativity amount of protons and electrons differ so we get an electric field or as we call it magnetic field. So if magnetic field is just an electric field how is it that the charge has to move so that magnetic field would exert a force on it? Electric field doesn't require that.

Consider the simpler case of a charge in empty space. If the charge is viewed from a stationary frame of reference, there is an electric field at any point in space (though it gets very small far from the charge) and nowhere in space is there a magnetic field.

If the same charge is viewed from a moving frame of reference, there are in general both electric and magnetic fields at any point in space. (I believe it's possible to have a zero mangetic field at some points in space, but in general there will be both.

The point of the example is not that the electric field is the same as the magnetic field, which is my interpretation of what you wrote. This is not correct. As another poster remarked, "what gave you the idea that this was true?".

The correct point of this example is that how one describes the electromagnetic field in terms of electric and magnetic parts (components) depends on one's choice of reference.

It's possible to compute how the electric and magnetic fields transform when one changes frames of reference - this is usually done at a fairly advanced level, though. If one knows the electric and magnetic fields at a particular point in space in one frame of reference, methods exist that allow one to compute the value of electric and magnetic fields as seen from the perspective of another frame of reference moving relative to the first.

For details, see the wiki article https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity for the equations about how the electric and magnetic fields in one frame of reference appear (transform) when seen from another frame of reference. The key point to understanding the equations is to first know that it is possible to find out the electric and magnetic fields in one frame of reference by knowing them in another. The equations simply document the procedure.

In the wiki article, he fields are split into a part parallel to the direction of relative motion (this uses the parallel synbol, $\parallel$), and a part perpendicular to this direction (this uses the symbol $\bot$). Then the equations give the parallel and perpendicular part of the electric and magnetic fields in one frame of reference in terms of the parallel and perpendicular parts in another frame of reference.

The equations may not be intuitive at first glance. One can accept them and move on, or one can study how they were derived. If one choses to accept them and move on (possibly to come back to the derivation later), one needs to make sure that one has chosen a reputable source to learn from, such as a textbook. Popular articles are not the best source for learning with this technique. Studying the derivations can be very rewarding if one has the patience and motivation to do so.

 

[sweet springs]

Hi. In a current carrying conductor because of special relativity amount of protons and electrons differ so we get an electric field or as we call it magnetic field.

Usually current wire is charged with excess or scarcity of electrons so that Poynting vector be generated in combination with electric field by surplus charge and magnetic field by current to carry energy along the wire.

So if magnetic field is just an electric field how is it that the charge has to move so that magnetic field would exert a force on it? Electric field doesn't require that.

We do not need density components of positive ions and electrons, but integrated 4-current (density) $(\rho, \mathbf{j})$ to consider Lorentz transformation. As above said by colleagues magnetic force does not reduced to electric force. They work in combination as $$F=q(E+v\times B)$$.

 

[SiennaTheGr8]

This is Edward Purcell's explanation of how magnetic fields arise from length contraction; you'll find a reasonably complete explanation of it here: http://physics.weber.edu/schroeder/mrr/mrrtalk.html. This is by no means a complete explanation of how magnetic fields arise; it is best thought of as a physical motivation for the more abstract and powerful methods that @Dale mentions above.

[emphasis added by me]

That crucial caveat is often left out, resulting in the misunderstanding that "electricity + length contraction = magnetism." Certainly this formulation doesn't explain electromagnetic waves, say.