  Planets with several Earth masses and a few day orbital periods have been
discovered through radial velocity and transit surveys. Regardless of their
formation mechanism, a key evolution issue is the efficiency of their retention
near their host stars. If these planets attained their present-day orbits
during or shortly after the T Tauri phase of their host stars, a large fraction
would have encountered intense stellar magnetic field. Since these planets have
a higher conductivity than the atmosphere of their stars, the magnetic flux
tube connecting the planet and host star would slip though the envelope of the
star faster than across the planet. The induced electro-motive force across the
planet's diameter leads to a potential drop which propagates along a flux tube
away from the planet with an Alfven speed. The foot of the flux tube sweeps
across the stellar surface and the potential drop drives a DC current analogous
to that proposed for the Io-Jupiter electrodynamic interaction. The ohmic
dissipation of this current produces potentially observable hot spots in the
star envelope. The current heats the planet and leads to a Lorrentz torque
which drives the planet's orbit to evolve toward circularization and
synchronization with the star's spin. The net effect is the damping of the
planet's orbital eccentricity. Around slowly (rapidly) spinning stars, this
process also causes rocky planets with periods less than a few days to undergo
orbital decay (expansion/stagnation) within a few Myr. In principle, this
effect can determine the retention efficiency of short-period hot Earths. We
also estimate the ohmic dissipation in these planets and show that it can lead
to severe structure evolution and potential loss of volatile material. However,
these effects may be significantly weakened by the reconnection of the induced
field [Slightly shortened abstract].
