Rotate in spherical coordinates

[daudaudaudau]

Hello !

In electromagnetics, the electric field of a small dipole in a spherical$$(r,\theta,\phi)$$ coordinate system is
$$E(\theta)=A\cdot \frac{e^{-jkr}}{r}\sin(\phi)\hat\phi$$

If the dipole is directed along the z-axis. (I used this geometry: http://mathworld.wolfram.com/SphericalCoordinates.html. Sometimes $$\theta$$ and $$\phi$$ are swapped.)

A is just a constant number.

My question is now: What if I want to know the field of a dipole, which is directed along the y-axis, or any axis? Is it possible to rotate $$E(\theta)$$ to make it point in any direction?

Cheers,
Anders

 

[mighty2000]

Hello Anders,

Thank you for your question. It is certainly possible to rotate the electric field of a dipole to make it point in any direction. This can be achieved by using the rotation matrix, which is a mathematical tool used to rotate vectors in three-dimensional space.

In order to rotate the electric field of the dipole, you would need to first determine the angle of rotation and the axis of rotation. This can be done by using the conversion between spherical coordinates and Cartesian coordinates.

Once you have determined the angle and axis of rotation, you can use the rotation matrix to rotate the electric field vector. The resulting vector will then be pointing in the desired direction.

I hope this helps answer your question. If you have any further inquiries, please let me know.