Electric Current: Present or Not?

[Razin Shaikh]

Consider a place where there is nothing but two point-like charges and you are the observer. If charges are moving then electric current is said to be flowing. In such place where there is no other reference, it cannot be distinguished whether charges are moving or the observer. In that situation, how can we know if electric current is present or not?

 

[Dale]

Hi Razin, welcome to PF!

Good question. Pick a reference frame. If the charge is moving in that frame then there is a current in that frame. Current is frame dependent for exactly the reason you have discovered.

 

[Tom_K]

If the current is in an electrically neutral wire, (equal number of positive and negative charges) there will always be current flow as seen by an observer from different frames of reference. In the frame where the electrons are moving the observer will detect a magnetic force field and in the frame where the electrons are at rest, there will be a flow of positive charges and the observer will detect an electric force field that is exactly equal to the magnetic force in the first frame, correct?

I suppose if we are considering isolated point charges this does not apply?

But if we are only considering isolated point charges flowing, wouldn't the observer be able to detect the magnetic field in any frame?

 

[jbriggs444]

But if we are only considering isolated point charges flowing, wouldn't the observer be able to detect the magnetic field in any frame?

In a frame of reference in which an isolated charge is stationary there is no magnetic field associated with that charge.

 

[Dale]

If the current is in an electrically neutral wire, (equal number of positive and negative charges) there will always be current flow as seen by an observer from different frames of reference.

An electrical source has an invariant $(\rho c)^2-j^2$. So if there is a frame where $\rho=0$, and $j\ne 0$, then this quantity will be negative in all frames and therefore $j\ne 0$ in all frames.

But if we are only considering isolated point charges flowing, wouldn't the observer be able to detect the magnetic field in any frame?

The fields have an invariant
$E^2-(cB)^2$. For an isolated point charge this field invariant is positive. So there exists a reference frame where each given location has $B=0$, but $E\ne 0$ in all frames.

 

[Tom_K]

In a frame of reference in which an isolated charge is stationary there is no magnetic field associated with that charge.

Yes, that must be true because B = μoI/2πr and with no relative velocity between charge and observer, no I and no B.

Yet, I am having difficulty conceptualizing this because I learned to think of a magnetic field in terms of lines of force, and these lines can even be shown to exist around a stationary magnet by sprinkling some iron filings on a sheet of paper and so they are tangible.

When it comes to these lines of force around a charged particle that is moving with respect to an observer, do they simply vanish when the observer starts moving with the charge?

 

[Tom_K]

An electrical source has an invariant $(\rho c)^2-j^2$. So if there is a frame where $\rho=0$, and $j\ne 0$, then this quantity will be negative in all frames and therefore $j\ne 0$ in all frames.The fields have an invariant
$E^2-(cB)^2$. For an isolated point charge this field invariant is positive. So there exists a reference frame where each given location has $B=0$, but $E\ne 0$ in all frames.

Yes, that helps, thank you. It seems the (cB)^2 term can be an analog of kinetic energy in some respect. Then it is easy to see why it will be zero in some frames.I still find it difficult to conceptualize those lines of force vanishing but I am probably over thinking this.

 

[sophiecentaur]

these lines can even be shown to exist around a stationary magnet by sprinkling some iron filings on a sheet of paper

That doesn't follow. The lines that you see are not the lines of force. They are the patterns of iron filings which are magnetised according to the existing field and interact in a certain way. They tend to join up with nearby particles which happen to have nearby N and S poles induced in them. That is not the same as having separate 'lines of force', which would have to be discrete entities.