A radioactive source in the form of a metal sphere of radius ${10}^{-2}m$ emits beta particles (electrons) at the rate of  $5\times {10}^{10}$  particles per second. The source is electrically insulated. How long will it take ( in  $\mu s$) for its potential to be raised by 2 V assuming that 40% of the emitted beta particles escape from the source.(electron charge $e=1.6\times {10}^{-19}c and \frac{1}{4\mathrm{\pi }{\in }_0}=9\times {10}^{9}N{m}^2{c}^{-2}$ )