Hello
To start off, the question deals with non relativistic system.
It is known that Biot-Savart law gives the magnetic field at position r (the position of the observer) , created by a current density at position r", if the current is static and the element is stationary in the observer rest frame. In the case of a time dependent current, one may use Jeffiminko equations to account for the delay.
However if the current element is moving with respect to the observer in a non inertial reference frame. Can we still use Jeffiminko equations ?
Thank you in advance
Hi Newgato,
I think Jefimenko's equation for B is still valid but its application is made more difficult by the fact that you have to determine at which point in space each current element is "seen" from point r at a certain time t. That's the same problem you are facing when you deal with moving electric charges.
In non-relativistic systems, the change of position during time t - t' can be neglected, so you can approximate the development of B in time by applying Jefimenko's equation to a series of quasi-resting current distributions.
Of course, if the current is carried by a conductor, and this conductor is electrically charged, then the movement of the charged conductor introduces an additional current.
Thank you for your answers, as you noted, my issue here is the frame in which I am writing the equations :
Should I use a field transformation since my current element is in a non-inertial reference frame even in nonrelativistc systemes ?
I take the next case (see picture).
What is the force exerted on the charge by the current element.
Using Jefimenko equations in the rest frame with no field transformation, this yielded (in my case) zero force, for these reasons :
- The current element is not charged and it doesn't depend on time so the electric field of the current element is zero, so Coulomb force is null.
- The charge is stationnary in its rest frame so Lorentz force is null.
This seemed wrong to me, since if the current element was moving in an inertial frame, I could use Lorentz transformation, which yields a force :
f = qvxB
Thank you
Hi Newgato,
in my opinion, if, in the rest frame of the current element, the current is constant, but seen from the rest frame of the charge, the current element is moving, then the d J(r', tr) / d t term in Jefimenko's equation for E is not zero because it is related to an r' which rests relative to the restframe of the charge, and at this point in space the current is not constant but changes direction and/or strength.
Exception: As long as the point in space coincides with the current element, and the movement of the current element is exactly parallel to its own axis, the current at this point is constant, and does not contribute to E.
Hi Joerg Fricke Thank you very much for the response, it was the time dependency of r', that I didn't see.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Electromagnetics
- Electromagnetic Fields