A hollow, conducting sphere with an outer radius fo $0\mathrm{.}250$ m and an inner radius of $0\mathrm{.}200$ m has a uniform surface charge density of $-3\mathrm{.}19$ microcoulomb$/$m$^2.$ When a charge is now introduced at the center of the cavity inside the sphere, the new charge density on the outside of the sphere is $-6\mathrm{.}37$