Correct Answer - 3
At `P`, due to cylinder
`E_(1) = (lambda)/(2 pi in_(0) . 2 R) = (rho pi R^(2))/(2 pi in_(0) . 2 R) = (rho R)/(4 in_(0))`
Due to sphere
`E_(1) = (1)/(4 pi in_(0)) .(rho . (4)/(3) (R//2)^(3))/((2R)^(2))= (rho R)/( 4 in_(0))`
`E_(1) - E_(2) = (rho R)/(in_(0)) [ (1)/(4) - (1)/(96)] = (23 rho R)/(96 in_(0)) = (23 rho R)/(16k in_(0))`
`k = 6`