A metal sphere with radius $1\mathrm{.}10$ cm

is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb

$=9\mathrm{.}10$ cm

$.$ Charge $+$q

is put on the inner sphere and charge $$q

on the outer spherical shell. The magnitude of q

is chosen to make the potential difference between the spheres $460$ V

$,$ with the inner sphere at higher potential. Calculate q

$.$ Are the electric field lines and equipotential surfaces mutually perpendicular? Are the equipotential surfaces closer together when the magnitude of E$$

is largest?