The capacitance of a spherical condenser is 1 μF. If the spacing between the two spheres is 1 mm, then the radius of the outer sphere is

Given : (b−a)=1×10−3m         ….(i)and C=4πε0abb−a=1×10−6⇒1×10−6=19×109ab10−3⇒ab=9                                  ….(ii)From equations (i) and (ii) b−9b=11000⇒1000b2−b−9000=0⇒b=1±(−1)2−4(1000)(−9000)2×1000  {Solving of quadratic equation}⇒b=1±36×1062000≈36×1062000=3m.