An electric field, passes through the surface of area having unit vector The electric flux for that surface is ____ Vm.

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Solution

Q.
An electric field, $\vec{E} = \frac{2 \hat{i} + 6 \hat{j} + 8 \hat{k}}{\sqrt{6}}$ passes through the surface of $4 m^{2}$ area having unit vector $\hat{n} = (\frac{2 \hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}) .$ The electric flux for that surface is ____ Vm. [2024]

Ans.
(12)

$ϕ = \vec{E} \cdot \vec{A} = (\frac{2 \hat{i} + 6 \hat{j} + 8 \hat{k}}{\sqrt{6}}) \cdot 4 (\frac{2 \hat{i} + \hat{j} + \hat{k}}{\sqrt{6}})$

$ϕ = \frac{4}{6} \times (4 + 6 + 8) = 12 Vm$

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