Question

The electric flux through the surface of a thin spherical shell of radius 6 cm, having a point charge 2 µC at its center is

• A. \( 36\pi \times 10^5 \, \text{N m}^2 \text{C}^{-1} \)
• B. \( 72\pi \times 10^5 \, \text{N m}^2 \text{C}^{-1} \)
• C. \( 36\pi \times 10^8 \, \text{N m}^2 \text{C}^{-1} \)
• D. \( 72\pi \times 10^3 \, \text{N m}^2 \text{C}^{-1} \)

Hint:

Electric flux through a closed surface depends only on the enclosed charge, not on the size or shape of the surface.

Answer 1

The Correct Option is D

From Gauss's law: \[ \Phi = \frac{q}{\varepsilon_0} \] Given \( q = 2\,\mu\text{C} = 2 \times 10^{-6} \, \text{C} \), and \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \) \[ \Phi = \frac{2 \times 10^{-6}}{8.85 \times 10^{-12}} \approx 2.26 \times 10^5 \, \text{N m}^2 \text{C}^{-1} \] Alternatively, using simplified constant-based format: \[ \Phi = \frac{2 \times 10^{-6}}{1/(4\pi \times 9 \times 10^9)} = 72\pi \times 10^3 \, \text{N m}^2 \text{C}^{-1} \]