Two point charges are initially $11$ cm apart and exert an electric force of $8$ N on each other. The charges are then moved to a new distance so that the force increases to $16$ N$.$ How large is the new distance? $($in cm$)$

A: $1\mathrm{.}1$ B: $2\mathrm{.}8$ C: $5\mathrm{.}5$ D: $7\mathrm{.}8$ E: $16$