How much electric flux will come out through | vedclass

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Question

(B) The electric flux $\phi$ through a surface is given by the dot product of the electric field vector $\vec{E}$ and the area vector $\vec{S}$.$\phi

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(B) The electric flux $\phi$ through a surface is given by the dot product of the electric field vector $\vec{E}$ and the area vector $\vec{S}$.$\phi = \vec{E} \cdot \vec{S}$Given $\vec{E} = 2\hat{i} + 4\hat{j} + 7\hat{k}$ and $\vec{S} = 10\hat{j}$.$\phi = (2\hat{i} + 4\hat{j} + 7\hat{k}) \cdot (10\hat{j})$Using the dot product properties $\hat{i} \cdot \hat{j} = 0$,$\hat{j} \cdot \hat{j} = 1$,and $\hat{k} \cdot \hat{j} = 0$:$\phi = (2 	imes 0) + (4 	imes 10) + (7 	imes 0)$$\phi = 0 + 40 + 0 = 40 	ext{ units}$.

How much electric flux will come out through a surface $S = 10\hat{j}$ kept in an electrostatic field $\vec{E} = 2\hat{i} + 4\hat{j} + 7\hat{k}$ units?

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