Need Jump Start On Two EM Questions

[mochi_melon]

1) I am asked to find the rate of radiation emitted from a charged particle with constant velocity moving through a magnetic field at an angle and then with an added parallel electric field. I know how to do it without the fields and just the point charge, I just don't know how to factor in the particle going through an E and B field.

However, I am inclined to believe that there is no radiation due just from the point charge because it is a constant velocity, making all the radiation from the field(s) it is in. Is this correct? Would the radiation just be the Poynting vector in that case (but if so, then it'd be zero before the addition of the parallel E field because you're taking the cross product of all zeros on the one side)

2) I am also asked to find the first non-zero multiple moment of a system for another problem (loop of radius r with alternating current). I'm not really sure what they mean by that, I have attached the formula for the magnetic moment, but I'm not sure what they mean by non-zero multiple.

Thanks!

 

[Jhero]

Thank you for your question about finding the rate of radiation emitted from a charged particle moving through a magnetic and electric field. Let me address your questions one by one.

1) First of all, you are correct in thinking that the radiation from a charged particle with constant velocity is due to the fields it is moving through, rather than the point charge itself. This is because a constant velocity means there is no acceleration, and radiation is only emitted when there is acceleration. Therefore, the radiation in this case would be due to the particle's interaction with the magnetic and electric fields.

To calculate the rate of radiation emitted, you will need to use the Larmor formula, which takes into account the particle's velocity, charge, and the strength of the magnetic and electric fields. The Poynting vector is indeed involved in the calculation, as it represents the direction and magnitude of the energy flow due to the electromagnetic fields.

2) The first non-zero multiple moment of a system refers to the lowest order of the system's multipole expansion that has a non-zero value. In the case of a loop of radius r with alternating current, the magnetic moment formula you have attached is an example of a multipole expansion. The first non-zero multiple moment in this case would be the dipole moment, which is the first term in the expansion.

I hope this helps clarify your understanding. If you have any further questions, please don't hesitate to ask.