Find the electric field at the center of a uniformly charged hemispherical shell of surface charge density sigma USING GAUSS LAW.

(a) Using Gauss law, drive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density $\sigma C/m^2$. Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative

(b)A uniformly charged conducting sphere of $2\times 5m$ in diameter has a surfaces density of $100mC/m^2$ . Calculate the (i) charge on the sphere (ii) total electric flux passing through the sphere.