Does displacement current create a magnetic field? And Lorentz force?

[greypilgrim]

Hi.

Does displacement current create a magnetic field by Biot-Savart? I googled and found contradictory answers.

Also, in the presence of an external magnetic field, is it meaningful to calculate a Lorentz force acting on displacement current? What does the force actually act on then?

 

[DaveE]

Does displacement current create a magnetic field

Yes. This is how radio waves can get from here to Jupiter.
It's also how a B-field antenna could receive that signal.

 

[greypilgrim]

I don't know what I was thinking when I asked the first question (it's right there in Ampère's law).

And what about $\vec{F}=I\cdot\vec{l}\times\vec{B}$? Can $I$ here be a displacement current?

 

[tech99]

Yes. This is how radio waves can get from here to Jupiter.
It's also how a B-field antenna could receive that signal.

I am not certain in my own mind if a displacement current is flowing in the case of a radio wave.

 

[DaveE]

I am not certain in my own mind if a displacement current is flowing in the case of a radio wave.

Yea, I get it. Me too. I've never really, really grokked displacement current. But it does have a changing E-Field in free space, just like the middle of a vacuum capacitor.

edit: I think you're right. Maxwells equations in free space don't include any current terms. It's about the separation of "bound" charges, I guess.

 

[PeterDonis]

I googled and found contradictory answers.

Where? Please give references.

 

[PeterDonis]

I am not certain in my own mind if a displacement current is flowing in the case of a radio wave.

It has to be. In fact, historically, it was Maxwell adding the displacement current to his equations that made it possible for those equations to predict electromagnetic radiation in vacuum.

The relevant Maxwell Equations are (omitting constants that depend on your choice of units):

$$
\nabla \times E = - dB / dt
$$

$$
\nabla \times B = J + dE / dt
$$

In vacuum $J = 0$ and these two equations can be used to derive a pair of wave equations that describe EM radiation in vacuum--but only if we include the displacement current $dE / dt$ in the second equation.

 

[PeterDonis]

Maxwells equations in free space don't include any current terms.

No $J$, yes. But they do include the $dE / dt$ term, which is the displacement current.

It's about the separation of "bound" charges, I guess.

Not in free space. In free space there are no charges.

 

[tech99]

I would have thought that a current is the movement of charges. There are no charges in a vacuum.

 

[PeterDonis]

I would have thought that a current is the movement of charges.

The term "current" has multiple meanings. Usually it refers to the $J$ in the second equation I wrote down. But the term "displacement current" refers to the $dE / dt$ term in that equation, which, as I have already explained, must be present for EM radiation in vacuum.

 

[Dale]

Does displacement current create a magnetic field by Biot-Savart?

No. The Biot-Savart law is for magnetostatic situations. So it assumes that there is no displacement current.