Question

I am trying to solve this problem from Griffiths, but my point is not really to ask the answer of this problem :

A point charge q is moving velocity v parallel to x axis. determine the total power passing through the plane at x=a when charge is at origin.

Now, I know how to find the fields in the frame for which charge is moving as stated, but for conceptual understanding I am interested in the following question:

Is energy delivered by EM field observer independent? In this case through the plane?

Intuitively, energy seems like a scalar, so I can guess that it would, but then if in the frame of problem there is power (there is), in the frame moving with the charge, there is no power delivered. Does this mean power through surface is not a scalar (the way it transforms)?

Note: When I compare power through surfaces in two frames, the second surface is the image of the initial surface after Lorentz boost.

Answer 1

The total power passing through a plane at x=a when a point charge q is moving with velocity v parallel to the x-axis can be determined using the concept of Poynting vector. The power delivered by the electromagnetic (EM) field is observer independent, including through the plane.

Step-by-step explanation:

The total power passing through a plane at x=a when a point charge q is moving with velocity v parallel to the x-axis can be determined using the concept of Poynting vector. The power delivered by the electromagnetic (EM) field is observer independent, including through the plane. Energy is indeed a scalar, but power is a vector quantity, representing the rate of energy transfer. In different frames of reference, the power through a surface can be different due to the Lorentz boost.