Question

A charge $Q$ placed at the center of a metallic spherical shell with inner and outer radii $R_1$ and $R_2$ respectively. The normal component of the electric field at any point on the Gaussian surface with radius between $R_1$ and $R_2$ will be

• A. zero
• B. $\dfrac{Q}{4\pi R_1^2}$
• C. $\dfrac{Q}{4\pi R_2^2}$
• D. $\dfrac{Q}{4\pi (R_1 - R_2)^2}$
• E. $\dfrac{Q}{4\pi (R_2 - R_1)^2}$

Hint:

Electric field inside any conductor in electrostatic equilibrium is always zero.

Answer 1

The Correct Option is A

Concept:
In electrostatics, the electric field inside a conductor is zero. Charges reside on the surface.

Step 1: Region between $R_1$ and $R_2$.
This region lies inside the conducting material.

Step 2: Electric field inside conductor.
\[ E = 0 \]

Step 3: Apply Gauss law.
Even though charge exists at center, induced charges cancel the field inside conductor. \[ \Rightarrow E = 0 \]