Question

$\sigma \epsilon$ / $2\epsilon_0$ (3) 2$\sigma \epsilon$ / ux associated with give 1

• A. $\sigma \epsilon$ / $2\epsilon_0$
• B. 2$\sigma \epsilon$

Answer 1

Option (2): $\displaystyle \frac{\sigma}{2\epsilon_0}$.

Answer 2

Using Gauss’s law for an infinite sheet of charge with surface charge density $\sigma$, we choose a “pillbox” Gaussian surface. The flux through both faces is

$$\Phi = 2EA.$$

Gauss’s law states that

$$\Phi = \frac{q_{\text{enc}}}{\epsilon_0} = \frac{\sigma A}{\epsilon_0}.$$

Equating the two,

$$2EA = \frac{\sigma A}{\epsilon_0} \quad \Longrightarrow \quad E = \frac{\sigma}{2\epsilon_0}.$$

Thus, among the given options, the correct expression is
(2) $\displaystyle \frac{\sigma}{2\epsilon_0}$.

Core Explanation (Minimal):

1. Choose a Gaussian pillbox through the sheet.
2. Total flux: $\Phi = 2EA$.
3. Enclosed charge: $q_{\text{enc}} = \sigma A$.
4. Gauss's law: $2EA = \sigma A / \epsilon_0$ ⟹ $E=\sigma/(2\epsilon_0)$.