Question

A point charge of +12 µC is at a distance 6 cm vertically above the centre of a square of side 12 cm. The magnitude of the electric flux through the square will be ________ × 10³ Nm²/C. 

Hint:

When a charge is placed at a height $a/2$ above the center of a square of side $a$, it can always be treated as being at the center of a Gaussian cube of side $a$.

Answer 1

Correct Answer: 226

Step 1: Imagine the square is one face of a cube with side $12 \text{ cm}$. The charge is at the exact center of this cube (6 cm from all faces).
Step 2: By Gauss's Law, total flux through cube $\Phi_{total} = \frac{q}{\varepsilon_0}$.
Step 3: Flux through one face $\Phi = \frac{q}{6\varepsilon_0} = \frac{12 \times 10^{-6}}{6 \times 8.854 \times 10^{-12}} = \frac{2 \times 10^6}{8.854} \approx 0.2258 \times 10^6 \text{ Nm}^2/\text{C}$.
Step 4: In the requested format: $225.8 \times 10^3 \approx 226 \times 10^3$.