A source in the form of a metal sphere of diameter 10-3 m emits electrons at a constant rate of 6.25 x 1010 particles per second. If the source is electrically insulated, how long (in μs) will it take for its potential to rise by 1.0 volt, assuming that 80% of emitted electrons escape from the surface.
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answer is 6.94.
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Detailed Solution
Capacitance of sphereC=4πε0R=0.5×10−39×109=118×10−12 FRate of escape of charge from surface=80100×6.25×1010×1.6×10−19=8×10−9 C/s20% remained with source only. so charge developed is same as electrons escaped.therefore, q=8×10-9t and q=CV⇒8×10−9t=118×10−12×1⇒t=10−128×10−9×18=10−3144=6.94 μs