But it was a constant force, not an oscillator, right?
It was some time ago that I did these things, but an approach could be to solve the equations of motion for x and px and then use the corners of the rectangle in phase space as starting conditions for 4 different trajectories. Then you can...
Hi
thanks a lot for the link! Very useful website :)
Ok, so my understanding after reading this solution is that the electromagnetic angular momentum that is radiated to infinity in time dt is contained in a spherical shell with radius r->inf. and thickness dr=c dt. So dL/dt is obtained by...
Hi!
OK, explicitly I think your integral would be (ignoring the first constant):
\int\frac{\partial g_{I}(-v_{1}t)}{\partial t}dt=
\int -v_1\, g'_I(-v_{1}t)dt
using the chain rule (yes if you want to write out the detalis we need it). Now putting x=-v1 t, and with dt=-dx/v1
=\int -v_1\...
Maybe I'm wrong, but I don't think you need to use the chain rule. Since you have no hidden t dependence in your functions I guess you can say
\int (\frac{\partial}{\partial t} f(z,t) )dt=f(z,t) + C
Differentiation and then integration with respect to t should give the same function back...
Homework Statement
9.8a) Show that a classical oscillating eletric dipole p with fields given by (9.18) radiates electromagnetic angular momentum to infinity at the rate
\frac{d\mathbf{L}}{dt}=\frac{k^3}{12\pi\epsilon_0}\textrm{Im}[\mathbf{p^*\times p}]
Hint: The electromagnetic angular...
Thanks for your replies, it was very helpful! Using section 5.6 of Jackson as you said I saw that I could show directly that the first integral
{\bf P_{field}}=-\frac{1}{c^2} \int {\bf (E(0)\cdot x) J)} d^3x
is equal to the sought answer without using the abc vector rule. Looking below eq...
Homework Statement
A localized electric charge distribution produces an electrostatic field,
{\bf E}=-\nabla \phi
Into this field is placed a small localized time-independent current density J(x) which generates a magnetic field H.
a) show that the momentum of these electromagnetic...