Principle behind electrostatic shielding?

[Dr.azwar]

if we have a solid conducting sphere with charges around it, then the elctric field inside the sphere is zero otherwise the electrons of the sphere would not be in equilibrium as there would be a net force acting on it. however if its a hollow sphere then why does the electric field inside the hollow sphere be zero?

 

[BvU]

Because the inside of the sphere is conducting, the potential is the same everywhere. There are no other sources of field or potential inside. No potential difference $\Rightarrow$ no electric field. Simple, isn't it ?

 

[Dr.azwar]

what if the hollow sphere is surrounded by charges, the field is still zero.how is that possible?(the empty space inside the hollow sphere is not conducting)

 

[BvU]

The empty space inside the hollow sphere is surrounded by an equipotential shell: the inside of the conducting sphere. No sources inside so the entire hollow sphere is at the same potential (*). Thus: no field.

Surrounding the conducting sphere with charges only causes an uneven charge distribution on the outside surface of the conducting sphere. Again, on that outside surface the potential has to be the same everywhere (otherwise the charges would simply move until it's the same). But on the outside there is a contribution from those external sources (charges).

(*) Note that that potential does not have to be zero: e.g. a lot of positive charges on the outside means that the inside surface charge is negative.

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[rude man]

if we have a solid conducting sphere with charges around it, then the elctric field inside the sphere is zero otherwise the electrons of the sphere would not be in equilibrium as there would be a net force acting on it. however if its a hollow sphere then why does the electric field inside the hollow sphere be zero?

The vector sum of the E field due to all the charges is zero inside the shell.

Same reason that, if you dig a hole into the Earth to a radius r' < R where R is the radius of the Earth, gravity at r' is due to the mass INSIDE r' only; mass at r > r' is - pardon the pun - immaterial.