Question

Find the Flux through the rectangular piece of area $10\text{cm}\times 20\text{cm}$, when placed in a uniform electric field intensity of $200\text{N/C}$ as shown in figure.

• A. $4{\text{Nm}}^2{\text{C}}^{-1}$
• B. $3.5{\text{Nm}}^2{\text{C}}^{-1}$
• C. $2.5{\text{Nm}}^2{\text{C}}^{-1}$
• D. Zero

Answer 1

The correct option is B $3.5{\text{Nm}}^2{\text{C}}^{-1}$

Given,
Electric field, $E=200\text{N/C}$

Area of the piece, $A=10\times 20=200{\text{cm}}^2\text{or}0.02{\text{m}}^2$

The best way to analyse the question is by looking into the side-on view of the diagram.


We can clearly see the angle between $\overrightarrow{E}$ and $\overrightarrow{A}$ is ${30}^{\circ }$

The flux through the surface,
$\varphi =|\overrightarrow{E}||\overrightarrow{A}|\cos \theta$

Substituting the values in the above equation,

$\varphi =200\times 0.02\times \cos {30}^{\circ }$

$\Rightarrow \varphi =\frac{200\times 2\times \sqrt{3}}{100\times 2}$

$\Rightarrow \varphi =2\sqrt{3}{\text{Nm}}^2{\text{C}}^{-1}$

$\therefore \varphi =3.46{\text{Nm}}^2{\text{C}}^{-1}\approx 3.5{\text{Nm}}^2{\text{C}}^{-1}$

Hence, option (b) is the correct alternative.