If an electric field is given by vec{E} = 10 | vedclass

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Question

(A) The electric flux $\phi$ is given by the dot product of the electric field $\vec{E}$ and the area vector $\vec{A}$.Given $\vec{E} = 10 \hat{i} + 3

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(A) The electric flux $\phi$ is given by the dot product of the electric field $\vec{E}$ and the area vector $\vec{A}$.Given $\vec{E} = 10 \hat{i} + 3 \hat{j} + 4 \hat{k}$.The surface lies in the $yz$-plane,so its area vector $\vec{A}$ is directed along the $x$-axis (normal to the $yz$-plane).Thus,$\vec{A} = 10 \hat{i}$.The electric flux is $\phi = \vec{E} \cdot \vec{A} = (10 \hat{i} + 3 \hat{j} + 4 \hat{k}) \cdot (10 \hat{i})$.Since $\hat{i} \cdot \hat{i} = 1$ and $\hat{i} \cdot \hat{j} = \hat{i} \cdot \hat{k} = 0$,we get $\phi = 10 	imes 10 = 100 	ext{ units}$.

If an electric field is given by $\vec{E} = 10 \hat{i} + 3 \hat{j} + 4 \hat{k}$,calculate the electric flux through a surface of area $A = 10 \text{ units}$ lying in the $yz$-plane.

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