So this can be figured out using the four-current density. This is the relativistic quantity that enters Maxwell's equations and transforms correctly between reference frames. In an inertial frame it is defined as ##\mathbf J=(c \rho,\vec j)## where ##\rho## is the charge density and ##\vec j## is the current density.Meow12 said:Suppose you have an infinite straight wire carrying electric current I. If you move in the direction of the electrons (opposite to the direction of the current) at the drift speed, would the current be zero in your new reference frame? Why or why not?
The wire is neutral (i.e., has 0 charge density in its interior) in the rest frame of the electrons. It's an often made wrong statement to claim it's neutral in the rest frame of the ion lattice. For details, see the newest version of my writeup about it:Orodruin said:No, it would not be zero because, while the (conduction) electrons are standing still, the rest of the wire (including all positive charges) is moving.
That doesn’t mean current is not different. Together with the charge density, current density forms a 4-vector called the 4-current density, which also transforms accordingly. For example, the wire will appear to have a net charge density in other frames even if neutral in its rest frame.
The wire can be any charge in any frame. The wire includes both the bulk charge (which behaves as you derived) and also the surface charge (which can be adjusted as desired). It is not a wrong statement, it is just a specification of boundary conditions.vanhees71 said:The wire is neutral (i.e., has 0 charge density in its interior) in the rest frame of the electrons. It's an often made wrong statement to claim it's neutral in the rest frame of the ion lattice.
Yes, electric currents can depend on the frame of reference. This is because the motion of charges that constitute the current can be perceived differently depending on the observer's frame of reference. According to the principles of special relativity, the observed current can change if the observer is moving relative to the charges.
Special relativity introduces the concept that the laws of physics, including electromagnetism, are the same in all inertial frames of reference. This means that an electric current observed in one frame of reference might be seen differently in another frame that is moving relative to the first. For example, a magnetic field in one frame can be transformed into an electric field in another frame, and vice versa.
Yes, an observer moving relative to the wire can measure a different current. This is because the relative motion can alter the density and velocity of the charge carriers as seen by the observer. The Lorentz transformation equations from special relativity describe how these quantities change between different frames of reference.
The Lorentz transformation equations are crucial for understanding how electric and magnetic fields transform between different inertial frames of reference. These transformations help predict how quantities like electric current and charge density will appear to observers moving at different velocities relative to the system being studied.
Yes, practical examples include scenarios in high-speed particle accelerators and astrophysical phenomena where relative velocities are significant. In such cases, the relative motion between observers and charged particles can lead to different measurements of currents and electromagnetic fields, demonstrating the importance of considering relativistic effects.