A thin metallic spherical shell of radius R carries a charge Q on its . . .

Question : A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge Q/2 is placed at its center C and another charge +2Q is placed outside the shell at a distance x from the centre as shown in the figure.

a) Find the electric flux through the shell.

b) Find the force on the charges at the centre C of the shell and at a point A.

Doubt by Aditya

Solution : 

a) Charge enclosed by the spherical shell (q_net) = Q/2

According to Gauss's Theorem 
Electric flux (ɸ_E) = q_net/ε₀

ɸ_E=(Q/2)/ε₀
ɸ_E=Q/2ε₀

b) We know,
Electric field inside a charged spehrical shell is Zero.
Force experienced by charge Q/2 at the centre C will be given by 

Force = charge × Electric field
F_C=(Q/2)×0
F_C = 0

We know,
Electric field due to a charged spherical shell at any point outside the spherical shell is given by 

E=kq/r²
E_A=k(Q+Q/2)/x²
E_A=k(3Q/2)/x²

Force experience by the charge 2Q at A will be
F_A=(2Q)×k(3Q/2)/x²
F_A=k3Q²/x²
F_A=(1/4πε₀)(3Q²/x²)
F_A = 3Q²/4πε₀x²