  A point charge in the presence of a metallic nanoshpere is a fundamental
setup, which has implications for Raman scattering, enhancement of spontaneous
emission of a molecule by an antenna, sensing, and modeling a metallic tip in
proximity to a nanoparticle. Here, we analytically expand the electric field of
a point charge in an $\epsilon_{2}$ host medium in the presence of an
$\epsilon_{1}$ sphere using the sphere eigenstates, where $\epsilon_1$ and
$\epsilon_2$ can take any values. Only the $m=0$ spherical harmonics are
employed in the expansion and the calculation of the potential and the electric
field is very simple. The electric field is strongly enhanced when
$\epsilon_{1}/\epsilon_2$ is close to an $(\epsilon_{1}/\epsilon_2)_l$
eigenvalue of a dominant mode, which is determined by the point charge location
and the measurement point. An electric field exists inside the sphere when
$\epsilon_{1}/\epsilon_2$ is close to a $(\epsilon_{1}/\epsilon_2)_l$ resonance
even when $\epsilon_1$ is a conductor. Low order modes generate an electric
field far away from the interface, where the $l=1$ mode with a resonance at
$\epsilon_1=-2\epsilon_2$ generates a field at the sphere center. The high
order modes which are associated with high spatial frequencies become more
dominant when the point charge approaches the sphere surface or when the
physical parameters are close the high order modes resonances. When
$\epsilon_{1}/\epsilon_2$ is smaller or larger than the eigenvalues of the
dominant modes, the modes interfere constructively and generate a strong signal
at an angular direction equal to that of the source. The spectral information
at the sphere surface may be utilized to calculate the point charge location
without knowing its magnitude.
