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I was thinking , if we have a uniform magnetic field and somehow it is moving with a velocity v . Assume that uniform magnetic field is spread over large area in comparison to size of charge and that magnetic field is somehow moving . Now if we make project a charge with same velocity v in that magnetic field will the charge experience any force ?Basically i am trying to understand that in the formula for force experienced by a charged particle in external magnetic field =q(V×B) the velocity V is in which frame . velocity is always relative to a given frame of reference. It never exists on its own. Is it with respect to the ground frame or is it with respect to the frame of magnetic field ?

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    $\begingroup$ What is a uniform moving magnetic field? $\endgroup$
    – user65081
    Commented Aug 5, 2021 at 15:14
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    $\begingroup$ There's no such thing as "the frame of the magnetic field" $\endgroup$
    – fqq
    Commented Aug 5, 2021 at 20:18

3 Answers 3

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Is it with respect to the ground frame or is it with respect to the frame of magnetic field ?

The $\vec{v}$ in the $q(\vec{v}\times\vec{B})$ equation is the velocity of the charged particle relative the inertial reference frame (IRF) from which the stipulated $\vec{B}$ field is observed from. From another IRF (the 'primed' frame), the $\vec{v}'$ and $\vec{B}'$ are generally different from $\vec{v}$ and $\vec{B}$.

This is because electric and magnetic fields transform between relatively moving IRFs. For example, if in some IRF, there is a purely electrostatic field, from another, relatively moving IRF, there is generally an associated magnetic field.

The key takeaway is that $\vec{B}$ is the magnetic field in the unprimed IRF while $\vec{B}'$ is the magnetic field in the primed IRF. Which one (if either) is the frame of the magnetic field? That is, is there such a thing?

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A charged particle moving inside a magnetic will experience a force depending on the charge of the particle,the velocity of the particle relative to a observer at rest and strength of the magnetic field. If you take a magnet and start moving the magnet at the same time the charge is moving the changing magnetic field of the magnet will induce a electric potential which may or may not affect the charged particle.

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If in the frame F there is only an uniform magnetic field $\mathbf B$, the velocity in the Lorentz force refers to this frame.

For example, the Earth magnetic field is uniform for a small area, as a lab room. What is relevant is the velocity with respect to the lab.

We can choose another frame F', with the same velocity of the charge, and from which the Earth is moving. But for this frame there is an electric field $\mathbf E$ besides $\mathbf B$. That explains why an observer in F' will also see the charge deflecting, in spite of it is at rest for him.

The components of the electromagnetic tensor change for different frames, and that means different values for $\mathbf E$ and $\mathbf B$.

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