I have a doubt related to magnetic field

Question

I have three doubts regarding the magnetic field due to the charge:-

Is a magnetic field generated when a charged particle moves with constant velocity or it only generated when the charge particle is accelerated or both?
Why and how does movement of charge result in the creation of a magnetic field around the particle?
We also know that motion is relative so if we observe in frame of moving charged particle then its magnetic field should not be there, then what we do in this case?
Note (related to third question): as we use pseudo force in non-inertial frame then what do we use in this case?

thanks for correcting my grammatical errors – ayu Aug 07 '23 at 14:17 — ayu, Aug 07 '23 at 14:17
Related : Magnetic field due to a single moving charge. – Frobenius Aug 07 '23 at 17:03 — Frobenius, Aug 07 '23 at 17:03

score 1 · Answer 1 · answered Aug 07 '23 at 14:24

1

The magnetic field is induced if the charge's velocity is non-zero. It doesn't matter whether the acceleration is zero or not.
As far as I know, there is no explanation for the why question, just a mathematical description of the process (Ampère's law, or, more generally, the Maxwell equations).
Yes, in the comoving frame there is no magnetic field, only the electric field. So the magnetic field strength is indeed frame dependent.

answered Aug 07 '23 at 14:24

Photon

4,847

2
"what we do in this case?" Answer: we come up with the special theory of relativity.

Kurt G.

Aug 07 '23 at 14:27

we don't have answer of 2nd ques in our modern physics ? – ayu Aug 07 '23 at 14:44

@ayu : please search a bit on PSE. I remember a recent post where an experienced physicist explained that the Maxwell equations don't say what is causing what. These equations relate $E,B$ fields charges and currents with each other. That's it. – Kurt G. Aug 07 '23 at 14:46

what is PSE? ohh by the way thanks for explaining – ayu Aug 07 '23 at 14:48

Physics Stack Exchange is PSE. ;) – Photon Aug 07 '23 at 15:11

Re 1) acceleration sometimes matter. Non-zero magnetic field does not require that the charge is moving or was moving with non-zero velocity at the time of production. Radiation component of electric field of a charged particle $\mathbf E_r$ is proportional to charge's acceleration, and in the first approximation, independent of velocity, so it is present/generated even if velocity is zero. Since radiation component of magnetic field is proportional to $\mathbf n \times \mathbf E_r$, the same is true for magnetic field. – Ján Lalinský Aug 08 '23 at 02:14

score 1 · Answer 2 · answered Aug 07 '23 at 14:27

1

Both.
We have observations of interactions between electric currents. We interpret these interactions using the "magnetic field" abstraction. A moving particle is a special case of this. There is no deeper "why": the phenomena demand certain things of a model, and "magnetic field" is the model that works.
The way our model captures this is that if I have a pure electric field in my frame of reference, an observer in motion relative to me sees a mix of magnetic and electric fields. Thus, while a stationary charge in my frame produces no magnetic field, it will produce a magnetic field in a frame moving relative to mine, just as you'd expect from a moving charge.

answered Aug 07 '23 at 14:27

John Doty

20,827

Technically, if in a moment of time the charge's velocity is zero but the acceleration isn't, there will be no magnetic field induced, so it's really about the velocity only, isn't it? – Photon Aug 07 '23 at 14:34
@Photon There will be little B field in the immediate vicinity of the charge, but there will be a propagating EM wave leaving the scene. – John Doty Aug 07 '23 at 14:41
so having a magnetic field in inertial frame, does not change total force or energy it (charged particle) contain in comparison of non -inertial frame? – ayu Aug 07 '23 at 14:42
@ayu Energy is frame-dependent, and in relativity, force is, too. – John Doty Aug 07 '23 at 15:04
@JohnDoty Agreed, but the propagating wave has been induced when the velocity was non-zero. I know, I'm fun at parties. ;) – Photon Aug 07 '23 at 15:44

score 1 · Answer 3 · answered Aug 07 '23 at 18:02

Your third question is the exact one that led Einstein and others to construct the Special Theory of Relativity. In traditional Maxwellian Electrodynamics, there are magnetic fields, electromotive forces, and other concepts that appear and disappear depending on the frame of motion used. Under Special Relativity, it turns out that a charged particle being motionless has a purely electric field. The same field in a moving frame has its electric field $\vec E$ Lorentz Transformed into an electric field $\vec E$ with a different value and a magnetic field $\vec B$. The $\vec E$ and $\vec B$ fields are motion-dependent components of a quantity called the EM Field Tensor $F_{\alpha \beta}$, which is not motion-dependent.

In the process of establishing this theoretical framework, they also made the discovery that other quantities such as elapsed time between events $t$ and spatial separation between objects $x$ are also motion-dependent. In the case of $t$ and $x$, the invariant quantity is the spacetime interval $s$ or equivalently the proper time $\tau$ of an observer. This ended up being the more Earth-shattering aspect of the theory, vis a vis the scientific community (not to mention everyday people).

I have a doubt related to magnetic field

3 Answers3