A point charge \(Q\) is placed inside a cavity within a solid isolated conducting sphere. Consider points \(A\), \(B\), and \(C\) as shown in the figure, where the magnitudes of the electric fields are \(E_A\), \(E_B\), and \(E_C\) respectively. The points \(B\) and \(C\) are at the same distance from the center of the solid sphere. The correct option is:
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The electric field inside a conductor is zero, but inside a cavity containing a charge it is generally non-zero.
Outside a spherical conductor, the field depends only on radial distance.
Step 1: Recall conductor electrostatics. A charge inside a cavity creates a real field within the cavity, the field inside the conducting material is zero, and outside the conductor the field looks like that of the total charge sitting at the centre. Step 2: Field at point A. Point $A$ lies inside the cavity which holds charge $Q$, so a non-zero field exists there: $E_A \neq 0$. Step 3: Locate B and C. Points $B$ and $C$ are both outside the sphere and at the same distance from its centre. Step 4: Use spherical symmetry outside. Outside an isolated conducting sphere, the field magnitude depends only on the distance from the centre, not on direction. Step 5: Compare B and C. Since $B$ and $C$ are equidistant from the centre, $E_B = E_C$. Step 6: Pick the option. Combining, $E_A \neq 0$ and $E_B = E_C$, which is option C. \[ \boxed{ E_A \neq 0,\; E_B = E_C } \]
