Question

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:

• A. \(E_A \neq 0,\; E_B \lt E_C\)
• B. \(E_A = 0,\; E_B = E_C\)
• C. \(E_A \neq 0,\; E_B = E_C\)
• D. \(E_A = 0,\; E_B \gt E_C\)

Hint:

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.

Answer 1

The Correct Option is C

Concept:

• A charge placed inside a cavity produces a non-zero electric field inside the cavity.

• The electric field inside the conducting material itself is zero.

• Outside the conductor, the field behaves as if the total charge were concentrated at the centre.

Step 1: Determine the field at point \(A\).
Point \(A\) lies inside the cavity containing charge \(Q\). Since the cavity contains an electric charge, the electric field inside the cavity is non-zero. Therefore, \[ E_A \neq 0 \]

Step 2: Determine the field at points \(B\) and \(C\).
Points \(B\) and \(C\) are outside the conducting sphere and are at the same distance from the centre. The external electric field of an isolated conducting sphere depends only on the distance from the centre. Hence, \[ E_B = E_C \]

Step 3: Choose the correct option.
\[ E_A \neq 0,\qquad E_B = E_C \] \[ \boxed{\text{Option (C)}} \]