In some problems of MHD we consider uniform horizontal or parallel to gravity magnetic fields. To simplify the Maxwell-Ampere equation we suppose that the magnetic field stay uniform and the lines of forces are not deformed with ions and electrons streamlines. Under these conditions the displacement current and the electric field are null, and there is no propagation of electromagnetic waves.
But in the reality the lines of the magnetic field are deformed with stream, and he varies with velocity and time.
The question is :
What are the conditions to have (or not) propagation of electromagnetic waves.
Thank you
Dear Haikel,
Perhaps I don't understand you properly, but the direction of the magnetic field that you might chose is independent of the displacement. This current is always very low, but it depends of the variations mainly of the electric field variation with respect to time. And the electric field is only zero if the density of electric charge is zero.
For having electromagnetic waves you need to have both electric and magnetic fields varying in time and the space. With these conditions you can reduce Maxwell equations to a wave equation which carries energy and momentum ( Poynting vector).
Dear Sir Daniel,
I thank you for your clear and constructive response.
Perhaps I should clarify my problem to have a more rich discussion.
In the problem we study, convection is not always stationary, and we have traveling (mechanical) waves along the domain filled by the liquid.
Please find attached figures clarifying the situation.
The liquid is flowing from the entry (at left side) to the right side, and it takes the form of transversal rolls (and sometimes three dimensional rolls) traveling in the streamwise direction.
When an constant magnetic field is imposed parallel to gravity :
1- Are the magnetic field lines will follow the streamlines (ions circulation), and the final magnetic fiel will be variable in space and time ?
2- If yes, can I still assume that electric field is zero? For now I do not solve equations allowing me to find the distribution of electrical charges.
Thank you.
Dear Haikel,
Let me try to answer your questions in a simple direct form.
1- Are the magnetic field lines will follow the streamlines (ions circulation), and the final magnetic fiel will be variable in space and time ?
If you have ions in circulation this means that you have electric field and also magnetic field due to the current associated to those ions. In this case the electric and the magnetic fields depend of the space and time and you can apply properly the Maxwell-Ampere law.
The stationary magnetic field parallel to the gravitational field doesn't enter in this Maxwell-Ampere law and only works for producing vortices on the ionic current.
2- If yes, can I still assume that electric field is zero? For now I do not solve equations allowing me to find the distribution of electrical charges.
No. Your electric field is not zero at all.
- Badges
- Science topic