Does a stationary charge feel a magnetic force when the wire moves?

[Dale]

Can you give me an example of a case where J is not related to v?

Any case where $\rho$ is not at rest in either frame.

I am going to make a guess as to what is happening here. You are looking at two pages, the “Classical Electromagnetism and Special Relativity” page and the “Current Density” page. Both pages use the symbol $v$, so you are trying to put the equations together. The problem is that the $v$ on each page has a different meaning. On the first page it says “The primed frame is moving relative to the unprimed frame at velocity $v$”. On the second page it says that $v$ is “the velocity of the charges”. Those two quantities are different in general.

You cannot go simply looking at symbols and mixing equations together. You need to understand what the symbol means in each context. The text and figures around the symbol usually explain, but from some of your questions it seems that you are either not reading or not paying attention to that important information.

 

[PhDnotForMe]

Any case where $\rho$ is not at rest in either frame.

I am going to make a guess as to what is happening here. You are looking at two pages, the “Classical Electromagnetism and Special Relativity” page and the “Current Density” page. Both pages use the symbol $v$, so you are trying to put the equations together. The problem is that the $v$ on each page has a different meaning. On the first page it says “The primed frame is moving relative to the unprimed frame at velocity $v$”. On the second page it says that $v$ is “the velocity of the charges”. Those two quantities are different in general.

You cannot go simply looking at symbols and mixing equations together. You need to understand what the symbol means in each context. The text and figures around the symbol usually explain, but from some of your questions it seems that you are either not reading or not paying attention to that important information.

Okay. So if I see a stationary proton and that proton begins to accelerate faster and faster in some direction, the B-field created will increase as it moves faster. Because the B-field changes, the E-field must change too. Will the transverse E-field of the proton increase or decrease?

 

[Dale]

Okay. So if I see a stationary proton and that proton begins to accelerate faster and faster in some direction, the B-field created will increase as it moves faster. Because the B-field changes, the E-field must change too. Will the transverse E-field of the proton increase or decrease?

See https://en.wikipedia.org/wiki/Liénard–Wiechert_potential in the section "Corresponding values of electric and magnetic fields". I don't know the answer to your question but that formula is how to calculate it.