Question

A thin metallic spherical shell of radius R carries a charge Q on it surface .A point charge Q/2 is placed at its centre C and an other chage 2Q is placed outside the shell at a distance x from the centre as shown in figure find (a) the force on the charge at the centre of shell and at the point A (b) the electric flux through the shell ​

Answer 1

Metallic Spherical shell means that we are talking about the sphere which is conducting. Now, conducting materials have an property that charge will be present only on there surface and no where else.

Now, charge kept at centre is Q/2, charge distributed on sphere is Q and charge outside is 2Q. We know, that, sphere is made up of metal, which have very high Dielectric constant value.

Force on charge Q/s due to 2Q will be given by the relation,

F = 1/4πε₀ × Q²/2 × 1/(R - t + t√k)²

This Relation is totally beyond the scope of 11th and 12th standard class. But Question was like that, thus i have written here.

This formula tells, if there is an extra medium of dielectric constant 'k' and thickness 't' kept in between of the air. Then the force will be as such.

Now, Sphere is of metal whose dielectric constant is infinite.

Thus F will be approximately tending to zero.

Now, you must have understood why in books it is always written that there will be no force acting on charge kept inside of metal due to the charge kept outside.

Now, similarly the charge on the sphere is outside and hence no force will be there on inner charge due to sphere also.

[Force may be created due to induction, but it  is usually not calculated.]

___________________________

(b). According to Gauss theorem, the electric flux is always due to the charge present inside of the Gaussian surface.

Now, 2Q charge will not effect Electric flux.

Electric flux = Net charge/ε₀

Net charge inside the Gaussian surface = Q + Q/2

= 3Q/2

Thus,

Φ = 3Q/2ε₀

Hope it helps.