$($a$).$ A positive charge $Q$ is uniformly distributed on a spherical surface of radius $R.$ Use Gauss law and derive the expression for the electric field $($magnitude and direction$)$ everywhere in space.

$($b$).$ Consider a system consisting of a charged spherical surface discussed in $($a$)$ and a positive point charge $2Q$ located at distance $3R$ from the center of a sphere, see figure. Find the magnitude and the direction of electric field at point $P,$ located half distance between the charge $2$ Q and the center of the sphere.