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A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge Q. Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

$\begin{array}{1 1} yes \\ no \\ none \;of\; the\; above \end{array} $

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A)
Solution :
yes
The electric field intensity inside a cavity is zero, even if the shell is not spherical and has any irregular shape. Take a closed loop such that a part of it is inside the cavity along a field line while the rest is inside the conductor. Net work done by the field in carrying a test charge over a closed loop is zero because the field inside the conductor is zero. Hence, electric field is zero, whatever is the shape.
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