Question

A uniform electric field of magnitude $E=100\text{N/C}$ exists in the space in $+x-$ direction. Calculate the flux of this field through a plane square of edge $10\text{cm}$ placed in the $y-z$ plane. Take the normal along the positive $x-$ axis to be positive.

• A. $1{\text{N-m}}^2/\text{C}$
• B. $2{\text{N-m}}^2/\text{C}$
• C. $3{\text{N-m}}^2/\text{C}$
• D. $4{\text{N-m}}^2/\text{C}$

Answer 1

The correct option is A $1{\text{N-m}}^2/\text{C}$

Given:
Edge of square, $a=10\text{cm}$
So, area of square
$A=a^2=100{\text{cm}}^2={10}^{-2}{\text{m}}^2$

Magnitude of electric field, $E=100\text{N/C}$


As positive normal to the square is along the positive $x-$ axis.

Thus, its angle with electric field,
$\theta =0^{\circ }$

Now, electric flux $\varphi$ is given by
$\varphi =\overrightarrow{E}\cdot \overrightarrow{A}=EA\cos \theta$

$\Rightarrow \varphi =100\times {10}^{-2}\times \cos 0^{\circ }=1{\text{N-m}}^2/\text{C}$