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1. Electric Charges and Fields
hard
Consider an electric field $\vec{E}=E_0 \hat{x}$, where $E_0$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is
A
$2 E_0 a^2$
B
$\sqrt{2} E_0 a^2$
C
$E_0 a^2$
D
$\frac{E_0 a^2}{\sqrt{2}}$
(IIT-2011)
Solution
$\dot{A}=A \cos 45^{\circ} \hat{i}-A \sin 45^{\circ} \hat{k}$
$=\sqrt{2} a^2 \frac{1}{\sqrt{2}} \hat{i}-\sqrt{2} a^2 \frac{1}{\sqrt{2}} \hat{k}=a^2 \hat{i}-a^2 \hat{k}$
$\phi=\dot{E} . \vec{A}=E_0 \hat{i} \cdot\left(a^2 \hat{i}-a^2 \hat{k}\right)=E_0 a^2$
Standard 12
Physics
