Final answer:
A uniformly charged spherical shell undergoing purely radial oscillations does not emit radiation and does not produce a magnetic field inside the shell.
Step-by-step explanation:
The statement in the question is true. A spherical shell that is uniformly charged and undergoes purely radial oscillations does not emit radiation. This is because for radiation to occur, there must be an acceleration of charged particles, which would result in the emission of electromagnetic waves. In the case of purely radial oscillations, the charged particles only move along the radial direction without any transverse acceleration, so no radiation is produced.
To show that there is no magnetic field, we can use Ampere's law. Since the current enclosed by any closed loop through the shell is zero (there are no currents inside the shell), the circulation of the magnetic field along any loop is also zero. This implies that the magnetic field inside the shell is zero as well.