Question

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

Answer 1

`P. alpha |dotoversetrarr(p)|^(2)` when
`oversetrarr(p) = sum e_(i) oversetrarr(r_(i)) = sum (e_(i))/(m_(i))m_(i)oversetrarr(r_(i)) = (e)/(m) sum m_(i)oversetrarr(r_(i))`
if `(e_(i))/(m_(i)) = (e)/(m) =` fixed
But `(d^(2))/(dt^(2))sum m_(i)oversetrarr(r_(i)) = 0` for a closed system
Hence `P = 0`.