Question

The electric field in the region is \(\overset{⃗}{E} = a\hat{i}+b\hat{j}\) where 'a' and 'b' are constants. The net electric flux passing through a square area of side 'l' parallel to Y-Z plane is

• A. \(al\)
• B. \(al^4\)
• C. \(al^6\)
• D. \(al^2\)

Hint:

Only the component of E along the normal to the area gives flux.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Flux through a flat area is \(\Phi = \vec E\cdot\vec A\). A square in the Y-Z plane has its normal along the x-axis, so \(\vec A = l^2\hat i\).

Step 2: Compute:
\[ \Phi = (a\hat i + b\hat j)\cdot(l^2\hat i) = a\,l^2 \]
The \(b\hat j\) part is parallel to the surface and gives no flux.

Step 3: Check:
Option (D) \(al^2\). Options (B) and (C) have wrong powers of \(l\), and (A) \(al\) has the units of a length rather than an area.

Final Answer:
Only the i component passes through the surface. \[ \boxed{\text{(D) }al^2} \]