Radiation from vibrating (rotating) ellipsoid

[Heirot]

Homework Statement

How to calculate the radiation from i) vibrating ii) rotating ellipsoid?

Homework Equations

The Attempt at a Solution

Rotating ellipsoid has a time dependant dipole moment so the radiation pattern will be of electric dipole type (The magnetic dipole and electric quadrupole are of higher order). What about vibration pattern? I'm tempted to say it will be electric quadrupole because of the change of quadrupole moment. But, during that change, a current exist and should give magnetic dipole radiation, shouldn't it?

 

[mark726]

Hello,

Calculating the radiation from a vibrating or rotating ellipsoid involves understanding the electromagnetic properties of the object and how they change over time. As you mentioned, a rotating ellipsoid will have a time-dependent dipole moment, meaning that its radiation pattern will be of electric dipole type. This is because the change in the dipole moment creates an oscillating electric field, which in turn produces radiation in the form of electromagnetic waves.

For a vibrating ellipsoid, the situation is a bit more complex. The vibration causes a change in the quadrupole moment of the object, which can produce radiation in the form of both magnetic and electric dipole radiation. The exact pattern of radiation will depend on the specific geometry and properties of the ellipsoid, and it may be a combination of both magnetic and electric dipoles.

To accurately calculate the radiation from a vibrating ellipsoid, you will need to take into account the changes in both the electric and magnetic fields over time, as well as the geometry and material properties of the object. This can be a complex task, and it may require advanced mathematical and computational techniques. If you are interested in learning more about this topic, I recommend looking into the theory of electromagnetic radiation and its applications to vibrating and rotating objects.

I hope this helps answer your question. Best of luck with your calculations!