The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) imes 10^3 \mathrm{~N} / \mathrm{C}$. The flux of the field through a rectangular surface parallel to $x-z$ plane is $6.0 \mathrm{Nm}^2 \mathrm{C}^{-1}$. The area of…

Question

The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) 	imes 10^3 \mathrm{~N} / \mathrm{C}$. The flux of the field through a rectangular surface parallel to $x-z$ plane is $6.0 \mathrm{Nm}^2 \mathrm{C}^{-1}$. The area of the surface is ________ $\mathrm{cm}^2$.

Aicharya · Accepted Answer

$\begin{aligned} & \phi=\overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{A}}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) 	imes 10^3 \cdot \mathrm{~A} \hat{\mathrm{j}} \ & 6=4 	imes 10^3 \mathrm{~A} \ & \mathrm{~A}=1.5 	imes 10^{-3} \mathrm{~m}^2 \ & =15 \mathrm{~cm}^2\end{aligned}$

The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(2 \hat{\mathrm{i}}+4…

Solution