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(D) The electric flux $\Phi$ through a surface is given by the dot product of the electric field vector $\overrightarrow{E}$ and the area vector $\ove

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(D) The electric flux $\Phi$ through a surface is given by the dot product of the electric field vector $\overrightarrow{E}$ and the area vector $\overrightarrow{A}$.$\Phi = \overrightarrow{E} \cdot \overrightarrow{A}$Given,$\overrightarrow{E} = (3 \hat{i} + 5 \hat{j} + 7 \hat{k}) 	ext{ NC}^{-1}$.The surface is in the $yz$-plane,so its area vector $\overrightarrow{A}$ is directed along the $x$-axis.Therefore,$\overrightarrow{A} = 3 \hat{i} 	ext{ m}^2$.Now,calculate the dot product:$\Phi = (3 \hat{i} + 5 \hat{j} + 7 \hat{k}) \cdot (3 \hat{i})$$\Phi = (3 	imes 3) (\hat{i} \cdot \hat{i}) + (5 	imes 0) + (7 	imes 0)$$\Phi = 9 	ext{ Nm}^2	ext{C}^{-1}$.Thus,the correct option is $D$.

In a region,the electric field is given by $\overrightarrow{E}=(3 \hat{i}+5 \hat{j}+7 \hat{k}) \text{ NC}^{-1}$. The electric flux through a surface of area $3 \text{ m}^2$ in the $yz$-plane is (in $SI$ units):

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