The injected excess electron concentration profile in the base region of an $npn$ BJT, biased in the active region, is linear, as shown in the figure. If the area of the emitter-base junction is $0.001\:cm^2 ,\mu_n=800cm^2/(V-s)$ in the base region and depletion layer widths are negligible, then the collector current $I_c$(in mA) at room temperature is _________
(Given: thermal voltage $V_T=26 \: mV$ at room temperature, electronic charge $q=1.6\times10^{-19}C$)