All Problems

Electromagnetic Waves. Radiation

Problem 4.211

Demonstrate that a closed system of charged non-relativistic particles with identical specific charges emits no dipole radiation.

Reveal Answer
4.211. The electric dipole moment of the system is p=∑eri=\mathbf{p}=\sum e \mathbf{r}_{i}= =(e/m)MrC,=(e / m) M \mathbf{r}_{C}, where MM is the mass of the system, rC\mathbf{r}_{C} is the radius vector of its centre of inertia. Since the radiation power P∝p2¨αP \propto \ddot{p^{2}} \alpha ∝r˙C2,\propto \dot{\mathbf{r}}_{C}^{2}, and in our case r¨C=0,P=0\ddot{\mathbf{r}}_{C}=0, P=0 too.
Prev
Next