Question

A uniform electric field is given as \(\vec{E}=4\times 10^{4}\hat{j}\ \text{N/C}\). The flux of this field through a square of side \(10\ \text{cm}\) whose plane is parallel to the Y-Z plane is

• A. \(400\ Vm\)
• B. \(200\ Vm\)
• C. zero
• D. \(1600\ Vm\)

Hint:

Flux is the dot product of field and area vector. The area vector of a square in the YZ plane points along the X-axis.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Electric flux is \(\Phi=\vec{E}\cdot\vec{A}\), where \(\vec{A}\) is perpendicular to the surface.

Step 2: Area vector
A square parallel to the Y-Z plane has its normal along the X-axis, so \(\vec{A}=A\hat{i}\).

Step 3: Calculation
\(\Phi=(4\times10^{4}\hat{j})\cdot(A\hat{i})=0\), since \(\hat{j}\cdot\hat{i}=0\).

Final Answer:
The flux is zero. \[ \boxed{\text{(C) }\text{zero}} \]