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I found here, it says "Ampere's Law roughly states that 'a changing electric field creates a magnetic field'.

(It does even have a \cite)

Even if it says "roughly states" think this is misleading, since it does not state if the strength or the direction of the magnetic field should change in order to produce a magnetic field.

Consider an example of current running through a wire. If the current is DC, the magnetic field does not change direction nor strength, but a magnetic field is created.

And in the first seconds of this video, it states the same. "A moving charge or current can create a magnetic field"

A similar question was made here and the first answer says: So we are forced to conclude that the magnetic field is due to the current itself, i.e. the movement of the charges, not any change in the electric field

So, i am not wrong i think. This statement is misleading, right?

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    $\begingroup$ There are two contributions to the curl of the magnetic field: one from the current density and one from the rate of change of the electric field. $\endgroup$
    – G. Smith
    Commented Feb 28, 2021 at 18:41
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    $\begingroup$ You could point this out on the wikipedia talk page, or just try editing the article, and see what the editors think. $\endgroup$
    – jklebes
    Commented Feb 28, 2021 at 18:42
  • $\begingroup$ it does not state if the strength or the direction of the magnetic field should change in order to produce a magnetic field. That doesn’t make sense. Did you mean for the first “magnetic” to be “electric”? Also, a change in a vector field always means a change in either or both the magnitude or the direction of the field. $\endgroup$
    – G. Smith
    Commented Feb 28, 2021 at 18:43
  • $\begingroup$ @G.Smith I know, it does not say what property of the electric field must change to create the magnetic field. Its strength (aka more amps on the wire) or its direction (aka AC current instead of DC) $\endgroup$
    – Christianidis Vasilis
    Commented Feb 28, 2021 at 18:46
  • $\begingroup$ You seem to be confusing electric field and current. You can have a changing electric field without any current, such as in a light wave. $\endgroup$
    – G. Smith
    Commented Feb 28, 2021 at 18:48

2 Answers 2

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On the same wikipedia page, there is a mathematically precise formula $$ \nabla \times \mathbf B = \mu_0 \mathbf J + \mu_0 \epsilon_0 \frac{\partial \mathbf E}{\partial t}, $$ which makes precise the notion that a changing electric field (i.e. $\partial \mathbf E / \partial t \neq \mathbf 0$) results in a magnetic field (if the curl of a field is non-zero, then the field has to be non-zero). If in addition there is also a current density (i.e. $\mathbf J \neq \mathbf 0$), then that also adds to the (curl of the) magnetic field $\mathbf B$.

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    $\begingroup$ Hmm thank you, yes you are right! the formula says it all. So the statement is correct, but it only describes 1/2 of the mathematical formula $\endgroup$
    – Christianidis Vasilis
    Commented Feb 28, 2021 at 18:51
  • $\begingroup$ Yes exactly. To give a bit more detail: it is mostly used in that way when we think of light propagating in a vaccuum: in a vaccuum there are no charges and hence no currents and so $\mathbf J = \mathbf 0$. Then Amperes law tells us that any changing electric field results in a magnetic field and Faraday's law then tells us that a changing magnetic field gives us an electric field again. You can put both equations together to find that the electric and magnetic fields propagate as a wave in the vacuum, one field creating the next. This electro-magnetic wave is light! $\endgroup$
    – Umut
    Commented Feb 28, 2021 at 18:55
  • $\begingroup$ @Umut, but when I look at an radio signal from a quasar, the E and B fields I detect on Earth can be traced but to charge and current densities 10 billion years ago, 10 billion light years away. $\endgroup$
    – JEB
    Commented Mar 1, 2021 at 3:41
  • $\begingroup$ @JEB In theory this need not be the case. The point is that electromagnetic waves can exist even in a space without any charges at all. This means that as far as I can tell there is no physical necessity that all EM waves in the universe were created by accelerating charges at some point in the past. $\endgroup$
    – Umut
    Commented Mar 2, 2021 at 2:27
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Charges and currents create potentials via:

$$ \phi(\vec r, t)=\frac 1 {4\pi\epsilon_0}\int \frac{\rho(\vec r', t_r)}{|\vec r-\vec r'|}d^3\vec r'$$

$$ \vec A(\vec r, t)=\frac {\mu_0} {4\pi}\int \frac{\vec J(\vec r', t_r)}{|\vec r-\vec r'|}d^3\vec r'$$

where

$$ t_r = t-\frac{|\vec r-\vec r'|}c $$

From there the fields follow. (See: https://en.wikipedia.org/wiki/Jefimenko%27s_equations).

So: fields are created by charge and current distributions from far away, long ago.

That the time derivative of the electric field is proportional to the curl of the magnetic field (locally), does not mean the electric field is creating the magnetic field, nor does it mean the magnetic field is creating the electric field. Is that even a Lorentz covariant concept?

Nevertheless, it may be useful to use such language when designing motors and generators.

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