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Question #42923

Difficulty: 8/10 | 🟢 Free

The Question

An infinite non-conducting flat sheet with a uniform surface charge density $\sigma > 0$ lies in the plane $3x + 4y = 0$ . The region $x > 0, y > 0$ also contains a uniform external electric field $\vec{E}_0 = E_0 \hat{j}$ . The electric potential at point $P(a, 0, 0)$ is found to be equal to the electric potential at point $Q(0, a, 0)$ , where $a > 0$ . What is the magnitude of the total electric flux through a flat rectangular surface of area $A$ that is parallel to the $xz$ -plane and located entirely within the region $x > 0, y > 0$ ? (Here $\varepsilon_0$ is the permittivity of free space).

Options

A.
$\frac{3\sigma A}{10\varepsilon_0}$
B.
$\frac{2\sigma A}{5\varepsilon_0}$
C.
$\frac{\sigma A}{10\varepsilon_0}$
D.
$\frac{\sigma A}{2\varepsilon_0}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Field due to Infinite Sheet|Potential Gradient Direction|Dot Product Geometry

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to handle vector fields in non-standard geometries, specifically targeting the misconception that the electric field of an infinite sheet can be treated purely as a scalar magnitude $E = \sigma/2\varepsilon_0$ .

Students often fail to calculate the correct unit normal vector for a tilted plane, leading to incorrect field components.

Furthermore, the problem requires applying the potential gradient relationship $\Delta V = -\vec{E} \cdot \Delta \vec{r}$ using a dot product rather than scalar distances.

A common trap is ignoring the external field or the sheet's tilt when calculating the final flux through the $xz$ -plane, leading students to erroneously select $\sigma A / 2\varepsilon_0$ or $2\sigma A / 5\varepsilon_0$ by only considering partial components of the system.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electric Charges and Fields - Class 12
Concept	Field due to Infinite Sheet
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free