Other radiation problems
An electric charge Q is distributed within a volume V, so that the
distribution is spherically symmetric for all times. The distribution
undergoes radial oscillations. Find the electric and magnetic fields
outside the volume, assuming that no other sources of electric or magnetic fields
are present anywhere in space.
Symmetry, Gauss' law, the Poynting vector
Gauss' law alone can be used in a situation with spherical symmetry
to find E and to determine that
B = 0.
- Details of the calculation:
Symmetry requires that E = E(r) r/r,
B = B(r) r/r.
Gauss' law: E(r)4πr2 = Qinside/ε0,
B(r)4πr2 = 0. (SI units)
E(r) = Qinside/(4πε0r2),
B(r) = 0.
S = (1/μ0)E×B
= 0 --> no radiation.