Charge attached to a spring

It's called the "reaction force" and is proportional to the "jerk" (the first time derivative of the velocity). For more info see textbooks. For example, Heitler's book: "The Quantum Theory of Radiation" the chapter on Classical Theory of Radiation section 4.

 

"acceleration" is the first derivative of velocity w.r.t. time. "jerk" is the time derivative of acceleration or the 2^nd derivative of velocity.

 

righto, that's what i meant to write--slip of the pen.

 

Hallo Adamecius
I am very attracted to springs. They are made of spiralling thread resistive of torsion, beacause bending of the thread itself is easy. This torsion has as counterpart: warming up. The dissipation must be in the warming up of the thread that is my answer.
greetings Janm

 

The concept of a charge on a spring is a good one, and the spring does not have to be dissipative for the system to lose energy. In Panofsky and Phillips "Classical Electricity and Magnetism" chapter 19 "Radiation from an Accelerated Charge" the authors go through the Lienard-Wiechert potential and vector triple products to show that there is a classical (non-quantum) field that drops off as 1/r and not 1/r^2, meaning power is being radiated. Panofsky and Phillips does have an equation giving the total radiated power of an accelerating electron (it has two terms proportional to acceleration squared) that can be put into the equation for an oscillating charge (with mass) on a spring.

 

Hello Bob
I have the second edition of the book and try to find out which equation you mean. Is it par. 19-4 "The "convection potential",
which starts with the Lorentz expression: F=e(E+u x B) and then equation (19-25)?
Years ago I studied the Lienard-Wiechert potentials a little, attracted to the concept that field-changes propagate with the velocity of light.
greetings Janm

 

I have the second printing (first edition) of Panofsky and Phillips dated August 1856. I was referring to equation 19-37 in paragraph 19-5 "Radiation with no restrictions on acceleration or velocity" on page 308. In my book, the paragraph on convection potential is # 18-4 on page 293.

 

So your book comes from 1856. 13 years after W.R.Hamilton found his quaternions and 17 years before maxwell wrote his "treatise on electricity and magnetism". I come back on the equations you mentioned and by the way my research of the Lienard Wiechert potentials is based on Laundau L.D. and Lifschitz : the classical theory of fields (translated from the Russian) A. Wesley 1960 par 62.