2

I know that an electrostatic (or magnetostatic) field does not depend on time but I was imagining to put a charge in a region of space. First there was no electrostatic field and then it appears, how does it all happen? There is a variation of the electrostatic field in the instant in which I create the aforementioned field, from 0 to a specific value. This variation is time dependant, so shouldn't it induce a magnetic field according to Ampere-Maxwell's law? I feel like I am missing something.

Dayane
  • 23
  • 4
  • Everything comes down to charges. Electrostatics assumes no time varying charge distributions which in turn means no time varying fields. To assemble charges into an eventual electrostatic configuration will require deviating from electro statics since while assembling the charges. – R. Romero Feb 02 '24 at 22:57
  • 1
    What do you mean by "put a charge". Are you moving it? Are you creating it (maybe splitting zero-net charge into a positive and (equally) negative charge, since it's hard/impossible to create net charge from zero charge? – basics Feb 02 '24 at 22:57
  • In my view this is a very thoughtful question that I've been thinking about as well. I'm sure we'd both appreciate an answer to the conundrum - why an apparent change in flux doesn't lead to induction? We need a person like Feynman who has the flight of thought to see things from a variety of perspectives, and discern how it relates to established principles. (Some days ago, I asked a question that was about 3/4 wrong in my understanding as I now learned, but unfortunately I didn't get any help in pinpointing why perspective was wrong - it was just dismissed. I later was able to figure it out – Daniel Feb 02 '24 at 23:12
  • I answered a very similar question: https://physics.stackexchange.com/a/799442/195949 – Claudio Saspinski Feb 03 '24 at 00:08
  • Sorry I was a bit overzealous, so I moved my own concern to a separate question, if it might be interesting to you as well: https://physics.stackexchange.com/questions/800032/induction-in-a-magnetostatic-scenario – Daniel Feb 03 '24 at 07:57

3 Answers3

1

I was imagining to put a charge in a region of space. First there was no electrostatic field and then it appears, how does it all happen?

This is not possible. It would violate the conservation of charge.

Instead, what can happen is that you can start with no charge and then you can make a pair of equal and opposite charges that are initially superimposed and then separate. The charges must move to separate, so it is not electrostatic. There is electromagnetic radiation, with the leading edge being standard dipole radiation

Dale
  • 99,825
  • You know, the question would hold if the two charges were already moving at a constant speed, passed each other in the middle (without changing pace), and continued onwards. The main point is that the OP says that a change in flux is occurring, yet no new fields are generated from it. That's the puzzle. The story about the charge appearing from nowhere, was a bit of a metaphor. – Daniel Feb 02 '24 at 23:28
  • 1
    @Daniel The OP's question as asked isn't physical since a net charge comes out of nowhere. However, as you point out, there are variations on the OP's question that makes sense. Dale's example is one. Yours is another, but actually a different situation than Dale's. In your scenario, there is no accelerated charge, so no radiation. However, there are time-dependent magnetic fields, since the current associated with a moving point charge is not stationary. One way to look at it is that a pure electric field becomes electric+magnetic under a Lorentz boost. – Andrew Feb 03 '24 at 00:07
  • See also https://physics.stackexchange.com/questions/412924/magnetic-field-due-to-a-single-moving-charge – Andrew Feb 03 '24 at 00:09
  • Thanks @Andrew for your comment. Yep, my situation is different than Dale's, it's just that I believe that was the deeper meaning behind the OP (given the frequent mention of the word static). "However, there are time-dependent magnetic fields, since the current associated with a moving point charge is not stationary." - yep, that's it. And we can assume the particle was travelling at constant speed long time, for 100 years even. My concern, and I believe that's the OP concern as well, is why an apparent change in E flux, doesn't induce a new field by "Ampere-Maxwell's law" in the OP's words? – Daniel Feb 03 '24 at 00:13
  • @Andrew I meant an apparent change in E flux from the motion at a constant speed. Let's say the particle is moving along the x-axis. Now it's at x=3, later it's at x=4. At, say, x=5 and y=1, there is an E flux change. Why as the OP says doesn't this induce a magnetic field by "by "Ampere-Maxwell's law"? If this could be simply explained, we'd be grateful I'm sure... – Daniel Feb 03 '24 at 00:14
  • My "theory" on the matter is that the H field from the movement just meets the requirement of the E flux change at (x=5, y=1), and therefore no additional fields are needed. At least it's an attempt to grapple with it. – Daniel Feb 03 '24 at 00:22
  • Andrew the link you've provided does say that per Biot-Savart law that a magnetic field is associated with a motion in constant velocity. To be sure... But the question is why doesn't this trigger induction given that both E and H flux change at points in space. – Daniel Feb 03 '24 at 00:31
  • @Daniel I don’t think that the OP’s question is about charges moving with constant velocity. But a moving charge certainly does “trigger induction”. The fields around a moving charge satisfy Maxwell’s equations – Dale Feb 03 '24 at 01:22
  • @Dale I agree that the question wasn't about a moving charge. It's tricky to get into the mind of a novice like me - they say, I see situations where there appears to be a change in flux, but no induction in response. Then the example was a little unlucky. It does seem as follows: curl of E = dB/dT (or similar equation). And curl of B = dE/dt (or similar equation). But these are not new things, but E and B here represent the magnetostatic fields and their rates of change as the particle moves. If that's true, my answer in words is also true. – Daniel Feb 03 '24 at 01:47
  • But when a novice (like me) hears induction, we expect something new. Here there is a movement of static fields, and golly gee, the their curls affirm their magnetostatic rate of change. Perhaps that can be called induction, but a novice, like me, wants something new to come out of induction, not the magnetostatic field. So I believe the answer to the question, that there is no need for new fields. The rate of change of magnetostatic fields or moving static fields affirms the induction expectation. – Daniel Feb 03 '24 at 01:50
  • @Daniel said “I see situations where there appears to be a change in flux, but no induction in response”. There are no such situations. Neither E nor B are static for a uniformly moving charge. It is not magnetostatic – Dale Feb 03 '24 at 01:52
  • I would agree with that, but the induction in response is not a brand new field. But the moving B field answers the induction requirement of the moving E field and vice versa. Would you say that's correct? – Daniel Feb 03 '24 at 01:55
  • @Daniel I have no idea what you mean by “a brand new field”. But other than that phrase, the rest seems fine. – Dale Feb 03 '24 at 02:48
  • @Dale I updated my answer - this view seems to be a bit in trouble unless you allow that a constant velocity travelling charge produces E fields that aren't radial. – Daniel Feb 03 '24 at 07:25
  • Sorry, I tend to be chatty, I moved my concern to a different question and I even wrote it mathematically and all... https://physics.stackexchange.com/questions/800032/induction-in-a-magnetostatic-scenario – Daniel Feb 03 '24 at 07:58
  • @Daniel you might benefit more from a discussion forum like physicsforums.com instead of a Q&A site like this. This one isn’t set up for discussion – Dale Feb 03 '24 at 13:22
0

There is a magnetic field while the electric field is being produced, but the magnetic field goes to zero when the electric field becomes static.

Jerrold Franklin
  • 1,748
0

You get an electrostatic field by separating charges, i.e. by moving electrons. You get a magnetostatic field by aligning the magnetic dipoles of the electrons, i.e. exactly the state that exists in a permanent magnet.

When an electrostatic field is created, doesn't it automatically generate an induced magnetic field?

We are talking about static fields, so we are neglecting the generation of these states. Then the answer is no. Both fields are absolutely independent of each other and are based solely on the fact that charges are equipped with the two intrinsic properties of an electric and a magnetic field.

HolgerFiedler
  • 10,334