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If a charge(+q) is placed at distance away from a hollow spherical conducting shell , would the net electric field inside the hollow portion remain zero? If the +q charge was placed anywhere inside the hollow portion , would the net electric field outside the hollow sphere be zero?

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If the charge is outside the hollow spherical conducting shell, the field inside the shell will be zero. The shell (or a closed conducting shell with a random form) will shield the field. The shell acts like a Faraday cage.

If the charge is inside the shell the field outside the shell will be the same as if there were no shell at all.

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  • $\begingroup$ Where is the third answer? $\endgroup$ – descheleschilder Jun 16 at 16:09
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would the net electric field inside the hollow portion remain zero?

The answer is yes, spherical or not spherical. The reason is that the bulk of the conducting shell is equipotential and as a consequence in any point within the cavity potential is also the same, then $\vec E=0$.

If the +q charge was placed anywhere inside the hollow portion, would the net electric field outside the hollow sphere be zero?

No. You find a total charge $+q$ distributed on the outer surface of the shell (and a charge $-q$ on the inner surface). If the outer surface is spherical the external field is the same as that due to a charge $+q$ placed in the centre. Note that this remains true whatever the position of internal charge.

The reason is that the external surface is equipotential, and by symmetry the external field is purely radial and only depending on distance from centre. Then apply Gauss' law.

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