A spherical conducting shell in an electric field field

[transparent]

If a spherical conducting shell is kept in an electric field (say, from a point charge kept at some distance outside the shell), will any charge be induced in the internal surface of the shell? Also what will the field be like inside the shell? Thanks.

 

[Jano L.]

If the interior of hte sphere does not contain free charge (usually the case if we did not put it there intentionally), the outer metallic shell of the sphere will shield the external field, so that in the metal and inside the sphere there is zero net field.

 

[transparent]

If the interior of hte sphere does not contain free charge (usually the case if we did not put it there intentionally), the outer metallic shell of the sphere will shield the external field, so that in the metal and inside the sphere there is zero net field.

Thanks. What about the charge? Will there be any charge on the inner surface of the shell? Also, how does the shielding effect work?

 

[Jano L.]

No. The shielding works this way: in static situation, there cannot be no currents in the metal, so electric field in the metal has to vanish. Due to Gauss' law, this also means there is zero charge density throughout the metal of the sphere. The only non-zero charge density can be at the surface and will be distributed in such a way so that it can completely cancel the external field.