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: Component along the normal:
The normal to the Y-Z plane is $\hat i$. The field component along it is $a$.

Step 2: Multiply by area:
Area is $l\times l = l^2$, so $\Phi = a\times l^2$.

Step 3: Result:
$\Phi = al^2$, option (D).

Final Answer:
The flux is a l^2. \[ \boxed{\text{(D) }al^2} \]