Why there is no monopole radiation in Electromagnetic field? I read somewhere that it is impossible because it violates charge conservation. I don't understand how? How charge conservation gets violated here?
Asked
Active
Viewed 2,513 times
3 Answers
10
In a multipole expansion of the electric potential, outside of some charge charge distribution $\rho(\mathbf r,t)$, the monopole term is simply
$$V_{mp}(\mathbf r) = \frac{Q_{total}}{4\pi \epsilon_0 r}$$
The associated electric field is then
$$\vec E_{mp} = \frac{Q_{total}}{4\pi \epsilon_0 r^2}\hat r$$
For this term to be time varying at some fixed $r$, the total charge must change with time, i.e., charge must be created or destroyed which is inconsistent with the conservation of electric charge.
So, if there were monopole EM radiation, charge would not be conserved and, further, such radiation would be longitudinal.
Alfred Centauri
- 60,633
5
It seems relevant to mention that a spherically symmetric solution of Maxwell equations (for a system with a spherically symmetric charge and current distributions) is necessarily static in a (not necessarily thin) vacuum shell (i.e. a region with no charges/matter). This is a consequence of the electromagnetic version of Birkhoff's theorem.
Qmechanic
- 220,844
-3
From quantum physics we know that Electrons have angular momentum l and that must be conserved (conservation of momentum) by emitted Photons which have a Spin of 1. There are no photons without spin (no spin= monopole) => therefore dipole radiation.
Hypothetical gravitons have a Spin of 2 (2x2 matrix). So gravitational waves are supposed to have a quadrupole moment
Randy Welt
- 552