A uniformly charged sphere of radius 0.1m has a charge of 2 microCoulomb uniformly distributed.Calculate electric field intensity at  0.05m from  centre of sphere ...Should n't intensity be zero in this case ?Please explain
 

Dear Student ,
You are right as the electric field intensity inside a spherical shell is zero .

Here in this case we can think a Gaussian surface inside the spherical surface at a radius of $0·05$ m centred at O and the total charge resides over the surface then the charge inside the spherical shell is zero .
Therefore according to the Gauss's theorem , the electric flux is , $$\begin{gathered} E ·4\pi {\left(0·05\right)}^2= 0 [q=0] \\ \Rightarrow E =0 \end{gathered}$$
Regards