Question

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

(i) Find the electric flux through the shell.

State the law used.

(ii) Find the force on the charges at the centre C of the shell and at the point A.

Answer 1

(i) 

(i) Electric flux through a Guassian surface, φ = \(\cfrac{Total\,enclosed\,charge}{\varepsilon_0}\)

Net charge enclosed inside the shell, q = 0

\(\therefore\)  Electric flux through the shell \(\cfrac{q}{\varepsilon_0}\) = 0

(ii) Guass's: Electric flux through a Gaussian surface is \(\cfrac1{\varepsilon_0}\) times the net charge enclosed within it.

Mathematically, 

(ii) We know that electric field or net charge inside the spherical conducting shell is zero. Hence, the force on charge Q/2 is zero.

Force on charge at A, F_A