Question

What is the electric field near an infinite plane sheet of charge density \( \sigma \)?

• A. \( \frac{\sigma}{2\varepsilon_0} \)
• B. \( \frac{\sigma A}{2\varepsilon_0} \)
• C. \( \frac{\sigma}{2\varepsilon_0 A} \)
• D. \( \frac{\sigma}{\varepsilon_0} \)

Hint:

Electric field due to an infinite sheet of charge is constant and given by \( \frac{\sigma}{2\varepsilon_0} \), independent of distance.

Answer 1

The Correct Option is A

To calculate electric field due to an infinite sheet of surface charge density \( \sigma \), we apply Gauss's Law: \[ \oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\varepsilon_0} \] Using a cylindrical Gaussian surface (pillbox): - Charge enclosed = \( \sigma A \) - Electric field is perpendicular to both surfaces, so flux is \( 2EA \) \[ 2EA = \frac{\sigma A}{\varepsilon_0} \Rightarrow E = \frac{\sigma}{2\varepsilon_0} \]